Pat chicken cutlets completely dry with paper towels. Season both sides evenly with kosher salt and black pepper.
Heat 1 tbsp olive oil in a 12-inch skillet over medium-high heat. Add the cutlets and sear undisturbed for 4 to 5 minutes per side until deeply golden and cooked through to 165°F (74°C). Transfer to a warm plate and tent with foil.
Lower heat to medium. Add the butter and remaining 1 tbsp olive oil to the skillet drippings. Add sliced onions and a pinch of salt. Cook, stirring regularly, for 10 to 12 minutes until soft, sweet, and deeply golden brown. Stir in garlic and fresh thyme for 60 seconds.
Pour in the beef broth, using a wooden spoon to scrape up all the caramelized browned bits (fond) from the pan surface. Simmer for 2 minutes until reduced by half.
Reduce heat to medium-low. Slowly stir in the heavy cream and simmer gently for 2 to 3 minutes until velvety. Nestle the chicken cutlets and plate juices back into the skillet. Top with shredded gruyère, cover with a lid for 2 minutes until bubbly and melted. Garnish with fresh thyme and serve hot.