Makes 4-6 servings
For the dough:
1 cup all-purpose flour
1/2 teaspoon salt (approx., I used a little bit less)
6 tablespoons unsalted butter, cut into small pieces and chilled
5 tablespoons ice cold water
For the filling:
2 tablespoons unsalted butter
2 tablespoons extra-virgin olive oil
2 1/2 pounds sweet onions, thinly sliced
6 thyme sprigs
Salt and freshly ground pepper
1 egg beaten with 1 tablespoon of milk or water for egg wash
To Make the Dough: In a bowl, whisk the flour with the salt. Using your fingers or a dough blender, rub the butter into the flour until the mixture resembles coarse meal. Drizzle the water over the flour and stir gently just until incorporated; gently press to form a dough. Flatten the dough into a disk, wrap in plastic and refrigerate for 1 hour.
Meanwhile, prepare the filling: In a skillet, melt the butter and olive oil. Add the onions and thyme and cook over moderately high heat, until softened, about 10 minutes. Reduce the heat to moderately low and cook, until the onions are golden, 20-40 minutes longer (note, the onions will continue to cook in the oven so it is not necessary to completely caramelize them). Remove from the heat and discard the thyme. Season with salt and pepper. Let cool.
Position a rack on the lowest rung and preheat the oven to 375 degrees. Line a large baking sheet with parchment paper or foil (if using foil, spray with cooking spray). On a floured work surface, roll out the dough to a 10-inch round and transfer to the baking sheet. Spread the onions on the round, leaving a 1 1/2-inch border. Fold the edge of the dough up and over the filling and brush the edge with the egg wash.
Bake the tart on the bottom shelf for about 40 minutes, until the dough is richly browned on the bottom.
Transfer the tart to the top shelf and bake for about 5 minutes longer, until the top of the crust is browned. Transfer the tart to a rack and let cool slightly. Cut the warm tart into wedges and serve.