Brown the beef. Set the Instant Pot to Sauté. Add the oil, then brown the ground beef in batches, breaking it into crumbles as it cooks. Transfer the browned beef to a plate and set aside. Repeat with remaining beef. Sauté the aromatics. Add the onion and jalapeño to the pot and cook until softened. Add the garlic and cook until fragrant, about 30 seconds.
Bloom the spices. Add the chili powder, cumin, coriander, oregano, salt, and pepper. Cook, stirring constantly, for about 30 seconds, just until fragrant. Careful not to burn.
Deglaze the pot. Pour in the beef broth and scrape the bottom of the pot thoroughly with a wooden spoon, loosening every browned bit. This is important to help prevent a burn notice.
Build the chili. Stir in the Better Than Bouillon, cocoa powder, instant coffee, and brown sugar. Return the browned beef to the pot, then add the kidney beans, pinto beans, and green chiles.
Layer the tomatoes. Pour the crushed tomatoes and tomato sauce over the mixture, then spoon the tomato paste over the top. Do not stir. Keeping the thicker tomato ingredients on top helps prevent them from scorching on the bottom of the pot.
Pressure cook. Secure the lid and turn the steam release valve to the Sealing position. Select Pressure Cook (or Manual on older models) and cook on High Pressure for 10 minutes.
Release the pressure. When the cooking cycle is complete, allow the pressure to release naturally for 10 minutes. Then carefully turn the steam release valve to Venting to release any remaining pressure.
Finish and serve. Once the pin drops, carefully open the lid away from you to avoid any remaining steam. Stir the chili thoroughly and adjust the seasoning to taste. Ladle into bowls and serve with your favorite toppings.