Onion Tart W Cheese Crust

["1. To make the filling, heat the olive oil in a heavy-bottomed pot over medium-high heat. Add the onions and saute for 2 minutes. Cover pot, reduce heat as low as it can go without shutting off, and let cook until onions have cooked down and released a lot of their liquid, about 20 minutes.", "2. Meanwhile, prepare the crust. Add the flour, salt, and paprika to the bowl of a food processor. Pulse once or twice to mix the dry ingredients. Add the cheese and butter, then pulse a few times until it forms a sandy-looking mixture. Add 1 tablespoon of seltzer, pulse again until a rough ball of dough comes together. If the mixture is too dry and crumbly, add more seltzer 1 teaspoon at a time (you may not need the entire 2 tablespoons), and continue to pulse until you have a ball of dough. Turn the dough out onto an unfloured counter, flatten and shape into a disk. Wrap in plastic wrap and chill for 30 minutes.", "3. Preheat the oven to 400u00b0F.", "4. Remove cover from the pot of onions, raise heat to medium, add the thyme and season with salt and pepper. Let the onions cook, stirring occasionally to scrape the browned bits from the bottom of the pot, until onions turn golden brown, about 30 to 35 minutes. When onions are golden and very tender, stir in the sherry vinegar. Remove from heat and, using a slotted spoon, transfer onions to a medium bowl.", "5. Place the chilled dough between two sheets of parchment paper, and roll it into a 13-inch circle. Fit dough into a 9-inch ungreased springform pan. Fold down sides of dough, leaving a 1-inch high crust.", "6. To finish the filling, add the egg and cheese to the bowl with the onions. Stir to mix well. Pour mixture over the tart crust and spread to the edges using a rubber spatula. Bake for 25 minutes, until slightly puffed and golden. Remove from oven and let cool for 5 to 10 minutes before slicing."]