Question Is the "Add Component" menu available via editor scripting?

Is there a built-in control that the "Add Component" menu uses as shown in the image below?

I need the same functionality, I just want fill it with different items and run my own code when an item is clicked.

 

I know it's been a few months now, but if you or anyone else is looking for it you'll want to use an AdvancedDropdown: https://docs.unity3d.com/ScriptReference/IMGUI.Controls.AdvancedDropdown.html

If you want to run code when an item is clicked, you just need to override the ItemSelected method.

(Edit)
I just want to point out that the ItemSelected method will only be fired once an AdvancedDropdownItem without any children is selected.