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Step 1
Preheat oven: Put a rack in the upper- and lower-third of the oven; preheat to 350°F (177°C).
Step 2
Drain tomatoes: Slice the tomatoes ¼-inch thick. Line a baking sheet with paper towel and arrange slices on top. Cover the tomatoes with another layer of paper towel. Let sit to drain.
Step 3
Mix Crust: Add oats to a food processor, pulse until the texture of coarse sand. Add sunflower seeds and salt, pulse until coarse sand. Add butter and pulse until butter is smaller than the size of peas. Add water, 1 tablespoon at a time, until the mixture comes together.
Step 4
Bake crust: Transfer the dough into 1 (9-inch) tart pan (ideally one with a removable bottom). Use your fingers to press the dough firmly into the bottom and up the sides. Use a fork to prick the bottom crust, about 15 times, to allow steam to escape. Bake on the lower rack until the crust is medium-firm to the touch, about 30 minutes (it'll take on a bit more color in the second bake). Remove and let cool.
Step 5
Bake tomatoes: Meanwhile, arrange the tomatoes on a parchment lined baking sheet. Brush with 1 tablespoon of the olive oil. Bake on the upper rack until the tops begin to wrinkle and brown at the edges, about 40 minutes.
Step 6
Mix cheese: Add ricotta and goat cheese to a medium bowl. Use a rubber spatula to mix the cheese until fluffy. Stir in basil, salt, and pepper (to taste).
Step 7
Assemble and bake: Spoon the filling into the cooled crust. Use a spatula to lift and arrange the tomatoes on top. Brush the tomatoes with the remaining 1 tablespoon olive oil and sprinkle with the garlic. Bake until the cheese is warm and crust is golden brown, about 20 minutes. Garnish with more pepper. Let cool slightly before slicing.