Combine flour, paprika, onion powder, and garlic powder in small shallow bowl. Set instant pot to brown setting.
Dredge short ribs in flour mixture, and begin browning the ribs in 2 Tbsps olive oil, 4 - 5 minutes on each side, or until golden brown. You will need to do this is batches.
After all the ribs are browned and removed from pot add onion and garlic, and stir. Cook for 3 - 5 minutes, until onion is getting soft and garlic is fragrant. Add carrots, and bell pepper and remaining Tbsp olive oil. Stir to coat veggies in the oil, and cook for 10 minutes.
Add can of tomato paste, and mix together with veggies. Cook additional 2 minutes to toast the tomato paste.
Add the wine, and stir until tomato paste and wine are combined. Let come to a simmer, and then add the crushed tomatoes and beef stock. Add dried herbs and a pinch of red pepper. Stir to combine
Return ribs to instant pot, and lock lid. Cook on high pressure for 1 hour and 5 minutes. Let the instant pot naturally release the pressure.
After the instant pot is finished and open, you will need to skim the top of the sauce with a large ladle to remove as much of the fat as possible. It's time consuming but worth it, I promise!
Remove all the ribs from the instant pot and begin shredding with two forks in a separate bowl, removing the bones. Return the shredded ribs to the instant pot and stir to combine.
Serve over your favorite pasta!