Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add butter and onion. Cook and stir until lightly browned, 1 to 2 minutes. Add cabbage and kielbasa; cook and stir until cabbage has wilted down, about 10 minutes. Add chicken broth and egg noodles; mix well.
Close and lock the lid. Select High pressure according to manufacturer's instructions; set timer for 3 minutes. Allow 10 to 15 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. Season with salt and pepper. Serve immediately.