These baked beans are made with Korean BBQ sauce and cooked long enough under pressure, with bacon, to develop a lovely smoky flavor.
Pour pinto beans in a large bowl and cover with cold water. Soak for 12 hours. Drain beans and rinse.
Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add bacon and shallots and cook until bacon is crisp and shallots soft, about 5 minutes. Drain and discard excess grease.
Pour chicken broth into the pot and bring to a boil. Deglaze the pot, scraping up browned bits from the bottom. Mix in paprika, mustard, salt, pepper, and bay leaf. Add brown sugar, ketchup, maple syrup, and Worcestershire sauce; mix to combine. Add drained pinto beans and Korean barbecue sauce and combine well. Cancel Saute mode. Close and lock the lid. Seal vent. Select Beans/Chili setting according to manufacturer's instructions. Set timer for 60 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, about 20 minutes. Unlock and remove the lid. Remove lid, stir beans, and check for doneness; beans should be soft. If more time is needed, close Instant Pot® again and pressure cook on "Manual" mode for an additional 20 minutes.