Preheat an oven. Heat a large skillet over high heat. When very hot, add olive oil. Meanwhile, pat chicken breasts dry with paper towels, then season generously on both sides with Kosher salt and black pepper.
Add the chicken breasts to the pan, then cook. The chicken should release easily from the pan when you go to flip it over. Cook on the second side.
Reduce the heat to medium, then add unsalted butter to the pan. Add thinly sliced onions, stir well, then cover with a lid. Cook, stirring occasionally, or until the onions have softened.
Increase the heat to medium-high, add flour. Stir until well absorbed, then deglaze with marsala wine and sherry vinegar. Use a spatula to scrape any browned bits off the bottom of the pan. Stir in chicken broth, Worcestershire sauce, and chopped thyme leaves. Bring to a boil.
Return the chicken to the pan, then sprinkle with shredded Gruyere cheese. Transfer to the oven and cook.
Garnish with additional fresh thyme and a pinch of flaky sea salt. Serve immediately with crusty bread on the side!