Generously grease a 24-cup mini muffin pan with cooking spray. In a large skillet over medium heat, heat oil and butter until butter is melted. Add onions; season with a generous pinch of salt and pepper. Cook, stirring often, until tender and caramelized, about 30 minutes.
Stir in broth and vinegar. Bring to a simmer and cook, stirring occasionally, until liquid is almost completely reduced but onions are still a little wet, about 5 minutes; season with salt and pepper, if needed. Remove from heat.
Preheat oven to 375°. Unroll 1 can of crescent roll dough. Cut along perforated line to make 2 pieces. Cut each piece lengthwise down the center to create 4 large rectangles (there should be a seam to guide you here). Cut each rectangle into 3 pieces. Press pieces into muffin cups, stretching as needed to completely cover the sides. Repeat with remaining can.
Spoon 1 tablespoon onion mixture into each cup. Sprinkle with cheese.
Bake bites until cheese is melted and dough is golden brown, 18 to 20 minutes.
Let cool 10 minutes in pan. Transfer bites to a platter. Top with thyme.
