Pat chicken cutlets thoroughly dry with paper towels. Season both sides with garlic powder, 1/2 teaspoon kosher salt, and black pepper.

Heat 1 tablespoon olive oil in a heavy 12-inch cast-iron or oven-safe skillet over medium-high heat (375°F / 190°C). Sear chicken undisturbed for 4 minutes per side until golden brown and almost cooked through. Transfer to a clean plate (the chicken will finish gently in the onion sauce).

Turn heat down to medium. Add butter and remaining 1 tablespoon olive oil directly into the skillet drippings. Add the sliced yellow onions, fresh thyme, and remaining 1/2 teaspoon kosher salt.

Cook for 18 to 20 minutes, stirring occasionally with a wooden spoon and scraping up the flavorful chicken fond from the pan bottom, until the onions collapse into deep golden brown, sweet caramelized perfection. Stir in minced garlic and cook for 1 minute until fragrant.

Sprinkle flour over the caramelized onions and stir constantly for 1 minute to cook out the raw flour taste.

Pour in the warm bone broth and apple cider vinegar, stirring vigorously to dissolve every bit of caramelized goodness from the bottom of the skillet. Bring to a steady simmer for 3 minutes until the gravy thickens nicely. Stir in the heavy cream until smooth.

Nestle the seared chicken cutlets and any accumulated resting juices back into the bubbling onion gravy in the skillet. Spoon a layer of caramelized onions over each cutlet, then generously top with the grated Gruyere and Swiss cheese.

Cover the skillet with a lid for 3 to 4 minutes on low heat until the cheese melts completely into a gooey blanket (or broil uncovered in the oven for 2 minutes at 450°F / 230°C until bubbling and golden-blistered). Garnish with fresh thyme leaves and serve immediately straight from the skillet!