Whisk 1/2 cup broth and egg together in a mixing bowl. Set aside.

Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add sausage and cook, breaking up with a spoon, for 3 minutes. Add butter, onion, celery, and water chestnuts. Cook 4 minutes more and turn pot off. Add parsley, salt, thyme, sage, and black pepper. Stir to combine. Add bread cubes to pot and pour egg mixture on top. Toss to combine.

Close and lock the lid. Select manual and set the timer for 6 minutes; allow 2 minutes for pressure to build. There will be no pressure to release in this step; when timer is up, carefully remove the lid and add remaining broth.

Close and lock the lid again. Select manual and set the timer for 5 minutes; allow 2 minutes for pressure to build. Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid.

Remove the lid and transfer dressing to a serving dish.