In a medium mixing bowl, stir together the almond flour, melted butter, egg, smoked paprika, and one cup (loosely packed) of the shredded cheddar. Press the dough evenly across the bottom of a 10-or-12-inch springform tart pan, pressing some of the dough partway up the sides of the pan. Bake the crust for 20-25 minutes, or until the edges are golden.
Sprinkle the remaining cheese evenly over the crust, and return it to the oven for an additional 8-10 minutes.
Arrange the tomato slices on the top of the crust. Sprinkle with salt and crushed red pepper, and garnish with basil. Serve immediately.