Step 1Thaw the dough in the refrigerator if frozen, then leave at room temperature long enough to roll out without cracking. Roll the dough into a square about 1/2-inch thick. Cut into 4 roughly equal squares and then roll them out until barely 1/8-inch thick, about 7 to 8 inches across. Place each on an 8- to 9-inch square of parchment paper, stack, cover and refrigerate.
Step 2Heat the oven to 400 degrees.
Step 3Warm the oil in a 12-inch skillet. Add the onions and a few pinches of salt. Cook over medium-high heat until some of the onions begin to color, 6 to 8 minutes. Stir, then cook another few minutes to color another layer of onions. Reduce the heat to medium-low and stir in the garlic, bay leaf and thyme. Continue cooking until the onions are lightly golden and tender but not mushy, 10 to 15 minutes. If they start to dry out, reduce the heat and cover the pan. Taste and adjust the salt. You should get about 1 1/4 cups. Cool completely. Remove the thyme and strip the leaves into the onions. Discard the bay leaf.
Step 4Allow the prepared dough to warm a few minutes just enough to fold the edges over without cracking. Place the squares of dough on their parchment on a baking sheet. Don't worry if the papers overlap. Prick the surface of each piece of dough lightly with a fork. Spread each piece with 4 to 5 tablespoons of the cooled onion mixture within an inch from the edge. Fold in the sides, mitering or lapping the corners. Press lightly to secure the sides and corners.
Step 5Bake until a rich golden brown, about 20 minutes. The edges of the onions may begin to caramelize.