Preheat your oven to the "keep warm" setting, which is about 170 degrees F.
Heat a dry 12-inch skillet
over medium high heat. You want it to get nice and hot, at least 3-5 minutes.
Meanwhile, prep your pork chops. Pat dry with paper towels. Use a sharp knife to snip the fat cap in 2 spots along the side of the chop. (See photo). Sometimes when you sear pork chops, the thick strip of fat constricts, causing the pork chop to curl up on itself, meaning it won't sear very well. Making cuts in the fat helps to avoid this curling. (The thinner your pork chops are, the more they will curl.)
Add the 1/4 cup flour, 1 tablespoon kosher salt, 1 tablespoon garlic powder, and 1/2 to 1 tablespoon black pepper to a shallow bowl or plate, and stir it all together.
Dredge each pork chop in the flour mixture, coating well and making sure to get the edges. Do NOT discard the flour mixture that is leftover! We're using it later.
When your skillet is very hot (medium high heat), add 1 tablespoon each butter and olive oil. When the butter is melted and the oil shimmers, add each pork chop. Do not crowd them together, make sure there is plenty of space in between each chop so that they brown instead of steam.
Sear over medium high heat for about 2 minutes, then turn the heat to medium and continue cooking for 2-3 minutes. When the chops are nice and brown on the bottom, flip each one, swirling the pan to spread around the fat as necessary. Cook on the second side over medium heat for another 4-5 minutes, depending on thickness, until a meat thermometer registers 140 degrees F. Depend on your meat thermometer more than the times.
Remove the pork chops to a baking sheet
and place in the warm oven. (this will not cook the chops, it's just to keep them nice and warm. You can just remove to a plate on the counter if you prefer.)
Cook the veggies. Add 2 tablespoons butter and 1 tablespoon olive oil to the still-hot skillet. (If you haven't prepped your veggies yet, turn off the heat).
Add the asparagus and mushrooms to the hot pan and cook over medium-high heat for 3-4 minutes, scraping up the browned bits from the pork, until the asparagus is crisp-tender.
Remove the veggies to the pan in the oven (or to a plate).
Return the pan to the burner over medium high heat, and add 2 tablespoons balsamic vinegar. Let it bubble for 30 seconds or so until it starts reducing, scraping up any bits.
Gradually add 1 cup chicken broth while stirring. Add 3 sprigs of thyme, or 1/2 teaspoon dried thyme.
Whisk in all the remaining flour mixture that you dredged the pork chops in. Simmer until there are bubbles all across the top, to make sure that any contamination from the flour is cooked out.
Reduce the heat to medium and gradually whisk in the cream.
Add the pork chops and the veggies back into the skillet, including any juices. Let the pan sauce simmer gently on medium or medium low heat until the sauce has thickened somewhat, another 2-5 minutes.