For the dough: In the bowl of a food processor fitted with the blade attachment, add the flour, sugar and salt. Pulse to combine. Add the butter and pulse until the butter is broken down into small pea-sized pieces. While continuing to pulse, slowly drizzle in the vinegar and then the water until a dough starts to form. Do not overmix. Remove the dough onto a sheet of plastic wrap. Form into a disc and allow to chill in the refrigerator for at least 1 hour.
For the filling: In the meantime, to remove the moisture from the tomatoes, slice the tomatoes in half and then again crosswise. Lay them down on several layers of paper towels lining a baking sheet. Salt the tomatoes and allow to sit for 30 minutes. This will remove excess water from the tomatoes that would otherwise make the tart dough soggy.
Preheat the oven to 375 degrees F.
Cut the cauliflower into tiny florets. Toss with the oil and 1 teaspoon salt and roast on a rimmed baking sheet until starting to brown, 15 to 20 minutes.
Remove the dough from the refrigerator. Flour a clean work surface and roll the dough out to 1/8 inch thick. Using a paring knife, cut the dough into eight 4-by-4-inch squares and place each piece onto a parchment-lined baking sheet.
Place 1 tablespoon manchego into the center of each square of dough. Top with a couple leaves of thyme. Lay 2 to 3 pieces cauliflower to one side of the cheese. Next to the cauliflower, place 2 slices of heirloom tomato. Once again, top with a sprinkle of manchego, thyme leaves and salt. Fold over the corners into the center of the tart. Pinch the sides together.
Bake until the dough is cooked through and golden brown, about 20 minutes. Let cool for 10 minutes before serving.