Pat the pork dry. Use paper towels to remove excess moisture from the surface. This helps the seasoning stick and gives the pork a better sear.
Season the pork. Mix the salt, paprika, garlic powder, black pepper, thyme, and rosemary, then rub the mixture evenly over the entire roast.
Heat the Instant Pot. Set the Instant Pot to Sauté and add the olive oil. Let the pot get properly hot before adding the pork.
Sear the pork. Place the pork in the pot and brown it on all sides for a few minutes. The goal is a deep golden-brown exterior, not to cook the center yet.
Remove the pork. Transfer the browned roast to a plate and keep it nearby while you prepare the cooking liquid.
Deglaze the pot. Pour in the chicken broth and scrape the browned bits from the bottom with a wooden or silicone spoon.
Add the flavor. Stir in the Worcestershire sauce, Dijon mustard, onion, and garlic.
Return the pork. Place the seared pork loin back into the Instant Pot.
Add the vegetables. Arrange the potatoes and thick carrot pieces around the pork. Keep the pieces fairly large so they hold their shape better during pressure cooking.
Pressure cook. Lock the lid, set the valve to Sealing, and cook on High Pressure for about 18 minutes for a 2–2½-pound roast.
Allow a natural release. Let the pressure release naturally for about 10 minutes, then carefully release any remaining pressure.
Check the pork temperature. Insert an instant-read thermometer into the thickest part of the roast. The pork should reach 145°F (63°C).
Rest the pork. Transfer the roast to a cutting board and let it rest for at least 3 minutes before slicing.
Slice against the grain. Cut the pork into even slices so the finished meat is easier to chew.
Serve with the vegetables. Spoon some of the flavorful cooking liquid over the pork and serve with the potatoes and carrots.