For the Onions:
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

For the Puffs:
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