Combine brown sugar, soy sauce, Worcestershire sauce, salt, garlic powder, black pepper, allspice, cinnamon, and liquid smoke in a bowl. Add oxtails and toss until well coated.
Turn on a multi-functional pressure cooker (such as Instant Pot) and select the Sauté function. When hot, add oil and place oxtails, flat-side down, inside. Brown on all sides, about 5 minutes. Transfer to a bowl and set aside.
Pour 2 tablespoons beef broth into the pot to deglaze, scraping up all the browned bits from the bottom with a wooden spoon. Add carrots, onion, green onions, garlic, and Scotch bonnet pepper. Sauté until onions have softened, about 5 minutes. Return oxtails to the pot with remaining beef broth, ketchup, and thyme. Cancel the Sauté function.
Close and lock the lid. Select high pressure according to the manufacturer's instructions; set the timer for 45 minutes. Allow 10 to 15 minutes for pressure to build.
Release the pressure using the natural-release method according to the manufacturer's instructions, 20 to 40 minutes. Unlock and remove the lid.
Remove oxtails and vegetables from the pot, leaving the liquid behind. Select Sauté function and bring liquid to a simmer. Combine water and cornstarch in a small bowl; stir into the simmering liquid. Add pinto beans and simmer until liquid is slightly thickened and beans are warmed, about 5 minutes. Return oxtails and vegetables back to the pot, and mix to combine.