Season short ribs with salt and pepper on both sides. Dredge in flour, shake off excess and set aside. Set a pressure cooker or multi-cooker to medium heat. Add canola oil. Sear beef on all sides until brown, about 10 minutes total.
To the pressure cooker, add the tomato paste, garlic, chopped tomatoes, chicken and beef stocks, carrots, and potatoes. Cover, lock on the lid and cook for 45 to 50 minutes. Release the steam from the cooker following the manufacturer's instructions, then remove the fork-tender beef and vegetables to a serving dish. Spoon the cooking broth over the top and serve.