Slice the leeks very thinly. Heat the olive oil over medium flame in a skillet. Add the leeks and cook and stir, helping to break up the leek rings with a wooden spoon. When they are soft, reduce the flame to low, add the water and cover. Cook for 10 minutes or so, adding water if needed to keep the leeks fairly moist.
In a blender place the tofu, lemon juice, salt and olive oil. Puree until very smooth, stopping to scrape down the sides or to help everything break up so the blender does its job.
Raise the oven heat to 375° F. Remove the lid from the leeks. Cook until the liquid evaporates and the leeks are very soft.
Scrape into the pre-baked crust. Sprinkle with 3 ounces of the cheese, about a third.
Pour the tofu filling over the cheese and spread to the edges. Distribute the remaining cheese over and to the edges of the tart. Sprinkle with the thyme, if using.
Bake until the tart is set, the filling has risen just a bit and the top has hints of golden color, 15 to 20 minutes.
Cool at least 10 minutes before cutting. Serve hot, at room temperature, or cold.