Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Crumble ground beef into the pot, and cook until browned, about 5 minutes.
Drain off any excess liquid. Sprinkle beef with salt and pepper. Pour in half the bone broth and tomato sauce. Add 1/2 of the chili beans to the pot.
Pour remaining bone broth and chill beans into a high power blender, such as a Vitamix®. Cover with lid and blend on High power for 30 seconds. Pour blended mixture into the Instant Pot®, but do not stir.
Close and lock the lid. Select high pressure according to manufacturer’s instructions; set timer for 5 minutes. Allow 10 to 15 minutes for pressure to build. Release pressure using the natural-release method according to manufacturer’s instructions, about 5 minutes. Release remaining pressure carefully using the quick-release method according to manufacturer’s instructions, about 5 minutes. Unlock and remove the lid.
Season with chili powder and stir to combine. Divide evenly into 4 bowls. Garnish with Cheddar cheese if desired.
