Blot chops dry with paper towels and season both sides with salt and pepper.

Heat 1 tablespoon olive oil and 1 tablespoon butter in a large nonstick skillet over medium-high heat. When butter sizzles, add chops and brown on both sides, 4 to 5 minutes per side. Remove chops from the skillet and keep warm.

To the same skillet, add remaining olive oil and butter. When butter is melted, add onions, mushrooms, and 1/2 teaspoon salt, and cook, stirring, until onions begin to turn translucent and mushrooms are softened, 4 to 5 minutes.

Stir in minced garlic and cook until fragrant, about 30 seconds. Add chicken stock, wine, and dried thyme, and bring to a boil.

Return chops and any accumulated juices to the skillet, nestling chops down into vegetables and broth. Remove about 1/4 cup of broth for later use. Cover, reduce heat to low, and cook until an instant-read thermometer inserted near the center reads 145 degrees F (63 degrees C), 4 to 5 minutes.

Stir cornstarch into the reserved cooking liquid, and stir until there are no lumps. While stirring the skillet sauce, add cornstarch mixture, and continue stirring 3 to 4 minutes, or until the sauce thickens.