Sprinkle both sides of chicken with Italian seasoning, garlic salt, and pepper.

Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. When pot is hot, add butter and oil and allow to butter to melt. Add chicken, working in batches if necessary, and cook until golden brown, about 3 minutes per side. Pour broth over chicken and press Cancel.

Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 3 minutes. Allow 10 minutes for pressure to build.

Release pressure using the natural-release method according to manufacturer's instructions for 20 minutes. Release remaining pressure carefully using the quick-release method, about 5 minutes. Unlock and remove the lid.