brew list and brew list --cask

Running brew list will show a list of all your installed Homebrew packages.

In addition, brew list --cask will provide the items installed using Homebrew Cask.

you could do something like this:

brew list <formula1> || brew install <formula1>

This will error on list and continue with install if not installed otherwise it will just list package files. (one could modify this further as a function or alias in .bashrc to make it easier to type)