French Onion Pastry Puffs

Name: French Onion Pastry Puffs
Ingredients: 2 medium yellow onions, peeled cut in half and sliced into 1/4-inch thick semi-circles; 3 tablespoon unsalted butter,softened, plus more for buttering the bread; 1 tablespoon olive oil; 1 scant teaspoon coarse sea salt; 1 teaspoon fresh thyme leaves; 1/2 teaspoon fresh cracked black pepper; pinch of granulated sugar; 3 tablespoons beef broth, beer, or white wine to deglaze the pan; 2 9×9-inch sheets all-butter puff pastry, thawed but still cold; 1 large egg, beaten; 2 tablespoons whole grain mustard; 1/3 cup finely grated Gruyère cheese