Add 2 teaspoons garlic powder, 1 ½ teaspoons onion powder, 1 ½ teaspoons salt, ½ teaspoon freshly ground black pepper, and 1 tablespoon brown sugar to small mixing bowl. Mix ingredients together until well blended.
Place 1 2-pound boneless pork shoulder roast on cutting board. Sprinkle half of spice mixture evenly over top of pork shoulder, then rub spices into meat. Flip pork roast over and repeat on other side, covering pork roast evenly and thoroughly with spice blend. Set pork roast aside.
Set Instant Pot to Sauté mode. Add 2 tablespoons unsalted butter to Instant Pot insert and let butter melt completely.
Once butter has melted, place pork roast in Instant Pot. Sear pork roast 3 minutes or until golden brown on bottom, then flip pork roast over and repeat. When pork roast is seared on both sides, transfer roast to cleaned cutting board and set aside.
If little or no liquid remains in bottom of insert, add 1 to 2 tablespoons butter to Instant Pot and let butter melt completely. Once melted, add 4 tablespoons minced fresh garlic and ½ cup chopped white onion to Instant Pot. Stir to incorporate, then sauté aromatics, stirring occasionally, approximately 5 minutes or until onions have softened.
Once onions have softened, add ½ cup dry white wine (or ½ cup chicken broth) to Instant Pot. Stir to incorporate wine, scraping bottom of pot to dislodge any browned bits of pork, garlic, or onions that may have stuck to insert.
Bring wine to boil, then boil wine 2 minutes.
After 2 minutes, add 1 cup chicken broth, 1 sprig fresh rosemary, 2 large carrots, 1 pound whole petite potatoes, 1 ½ teaspoons Dijon mustard, and ½ teaspoon dried thyme to Instant Pot. Stir until ingredients are fully incorporated.
Return seared pork roast to Instant Pot and nestle pork roast in broth mixture. Pork roast does not need to be fully submerged.
Secure lid on Instant Pot with and lock lid with valve in Sealing position. Set Instant Pot to Manual High Pressure mode, then set cook time to 30 minutes. Instant Pot will pressurize and then 30-minute cook time will begin.
When 30-minute cook time ends, Natural Release pressure for 10 minutes.
When 10-minute Natural Release ends, immediately and carefully Quick Release any remaining pressure, then remove lid and set aside.
Use tongs to carefully transfer pork shoulder to large bowl, then use slotted spoon to transfer potatoes and carrots to same bowl. Set aside.
Add 2 tablespoons cornstarch and 2 tablespoons cold water to small mixing bowl. Whisk ingredients together vigorously until fully combined, forming smooth cornstarch slurry.
Set Instant Pot to Sauté mode and add prepared cornstarch slurry to insert. Stir slurry into gravy until incorporated, then simmer gravy 3 to 5 minutes or until thickened.
Optional: Let pork roast rest 5 minutes, then chop, shred, or slice pork roast before returning roast to Instant Pot.
Once gravy has thickened, turn Instant Pot off. Return vegetables and pork roast to Instant Pot. Spoon gravy over pork roast, then serve warm. Alternately, arrange roast and vegetables on serving platter. Spoon gravy over top of roast or transfer gravy to serving container. Serve warm.