Pat the ribs dry with paper towels and season on all sides with salt and pepper. Set aside.
Select the "Sauté" function on your Instant Pot and heat the olive oil. Once hot, add the ribs to the pot in a single layer. Do this in batches if necessary so as not to crowd the pot. Brown the ribs on both sides for about 5-7 minutes total. Transfer the browned ribs to a platter.
Add the chopped onion and carrots to the pot; cook for 2 to 3 minutes, then add minced garlic. Sauté until soft and fragrant.
Stir in the beef broth, balsamic vinegar, tomato paste, and chopped fresh thyme. Stir well to combine the ingredients.
Return the short ribs to the Instant Pot, ensuring they are fully submerged in the sauce. Add the bay leaves.
Close the Instant Pot lid and set the pressure release valve to the "Sealing" position.
Select the "Pressure Cook" function and set the timer for 45 minutes on high pressure.
Once the cooking time is complete, allow the pressure to naturally release for 10 minutes. Then, carefully do a quick release to release any remaining pressure.
Open the Instant Pot lid and remove the short ribs, placing them on a serving platter. Cover to keep warm.
Strain the broth into a pot through a sieve, then return the broth to the Instant Pot. Whisk the cornstarch with water until smooth; whisk in the honey until incorporated, and add the cornstarch liquid to the instant pot.
Select the "Sauté" function again and set the timer for 10 minutes. Let the sauce simmer until it thickens. Make sure to stir frequently.
Pour the thickened sauce over the short ribs, tossing to coat them evenly.
Serve the Instant Pot short ribs hot, garnished with fresh chopped parsley.