Preheat oven to 350°F. Coat a 9x13-inch baking dish with cooking spray.
Combine thyme, dried parsley, garlic salt, dried oregano, cayenne, and dry mustard in a shallow bowl. (If you don't want any heat, the cayenne may be omitted altogether. If you prefer things hotter, increase to ½ teaspoon.)
Arrange half the sliced onions evenly in the prepared baking dish to cover the base. Sprinkle with half of the combined spices, then arrange half of the butter pieces and half of the cheeses on top. Repeat with remaining onions, spices, butter, and cheeses to create a second layer.
Cover with aluminum foil and bake until onions are soft and sides are bubbly, about 40 minutes. Remove foil and bake until top is golden, about 15-30 minutes. Serve alongside grilled steaks, barbecue, with burgers, or as a savory side dish to complement any meal.
