Preheat your oven to 450°F, positioning the rack in the upper third.
In a small bowl, whisk together olive oil, 1 tablespoon melted butter, 1 tablespoon thyme, salt, and pepper.
Arrange the onion slices in an even layer in a broiler-safe 9-by-13-inch metal baking pan. Brush the butter mixture over the onions.
Roast for 30 minutes, flipping the onions once halfway, until golden and slightly tender.
In the same small bowl, combine panko breadcrumbs with the remaining melted butter and ½ teaspoon thyme. Toast the mixture in a skillet over medium-high heat for 2-3 minutes until golden and fragrant. Set aside.
Flip the onions again, then pour in the beef broth and vinegar. Roast for an additional 10 minutes until the liquid reduces and the onions are soft.
Switch the oven to broil. Sprinkle the cheeses evenly over the onions, and broil for 1 minute until melted and bubbling.
Top with the reserved panko mixture and garnish with thyme leaves before serving. Enjoy as-is or alongside a fresh salad for a complete meal!