Once a program is deemed "worthy" to appear on the front page of the Start menu, Windows selects the most frequently-used shortcut as the one to appear on the front page of the Start menu.

So, for example, say you run cmd.exe 100 times from anywhere (Run box, desktop shortcut, etc.), and Windows determines it is used frequently enough to warrant appearing on the front page of the Start menu. Now, when looking at all of your shortcuts on your Start menu that point to cmd.exe, Windows knows you've used the Visual Studio cmd.exe shortcut once and the one in Accessories zero times, the Visual Studio one is used, because it is the most frequently-used shortcut, even though that's not typically how you run cmd.exe. The rules for this weighting are not public, so we don't know what happens if all shortcuts are used zero times. Some other part of the algorithm would determine that the VS shortcut is the winner.

This explains why, when you run it from Accessories, that shorcut eventually appears instead of the VS one. Eventually might have been once, might have been 10 times. Again, the exact algorithm is a mystery to outside-MS people.

Raymond Chen has a series of blog posts explaining how this works:

What determines which programs show up on the front page of the Windows XP Start menu?

Use Powershell Remoting:

Updated link: https://docs.microsoft.com/en-us/powershell/scripting/learn/remoting/running-remote-commands?view=powershell-7

Copy pasted form an older version:

Windows PowerShell Remoting

Windows PowerShell remoting, which uses the WS-Management protocol, lets you run any Windows PowerShell command on one or many remote computers. It lets you establish persistent connections, start 1:1 interactive sessions, and run scripts on multiple computers. To use Windows PowerShell remoting, the remote computer must be configured for remote management. After you have configured Windows PowerShell remoting, many remoting strategies are available to you. The remainder of this document lists just a few of them. #Start an Interactive Session To start an interactive session with a single remote computer, use the Enter-PSSession cmdlet. For example, to start an interactive session with the Server01 remote computer, type:

Enter-PSSession Server01

The command prompt changes to display the name of the computer to which you are connected. From then on, any commands that you type at the prompt run on the remote computer and the results are displayed on the local computer.

To end the interactive session, type:

Exit-PSSession

#Run a Remote Command

To run any command on one or many remote computers, use the Invoke-Command cmdlet. For example, to run a Get-UICulture command on the Server01 and Server02 remote computers, type:

invoke-command -computername Server01, Server02 {get-UICulture}

The output is returned to your computer.

LCID    Name     DisplayName               PSComputerName
----    ----     -----------               --------------
1033    en-US    English (United States)   server01.corp.fabrikam.com
1033    en-US    English (United States)   server02.corp.fabrikam.com

#Run a Script

To run a script on one or many remote computers, use the FilePath parameter of the Invoke-Command cmdlet. The script must be on or accessible to your local computer. The results are returned to your local computer.

For example, the following command runs the DiskCollect.ps1 script on the Server01 and Server02 remote computers.

invoke-command -computername Server01, Server02 -filepath c:\Scripts\DiskCollect.ps1

#Establish a Persistent Connection

To run a series of related commands that share data, create a session on the remote computer and then use the Invoke-Command cmdlet to run commands in the session that you create. To create a remote session, use the New-PSSession cmdlet.

For example, the following command creates a remote session on the Server01 computer and another remote session on the Server02 computer. It saves the session objects in the $s variable.

$s = new-pssession -computername Server01, Server02

Now that the sessions are established, you can run any command in them. And because the sessions are persistent, you can collect data in one command and use it in a subsequent command.

For example, the following command runs a Get-Hotfix command in the sessions in the $s variable and it saves the results in the $h variable. The $h variable is created in each of the sessions in $s, but it does not exist in the local session.

invoke-command -session $s {$h = get-hotfix}

Now you can use the data in the $h variable in subsequent commands, such as the following one. The results are displayed on the local computer.

invoke-command -session $s {$h | where {$_.installedby -ne "NTAUTHORITY\SYSTEM"} }