I’d like to create and edittext box with a custom offset background like this:

How should I go about doing this?
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I’d go with a LinearLayout containing your border as the background drawable, same padding for top, left and right and higher padding at bottom.
Then, setting a custom, stateful 9-patch drawable for your EditText based on your background.
In fact, if you make your background 9-patched, you can use it both in your LinearLayout and your EditText.
Also, you don’t have to make your EditText drawable stateful; but I strongly advise you to do so, so the user can actually get visual feedback from your EditText.
Sample code:
layout/your_layout.xml
drawable/bg_border_statelist.xml
Assuming your background image is 9-patch and called
bg_border.9.png, and the respective 9-patch version is calledbg_border_selected.9.png.Cheers!