Step 1

Preheat oven to 400 degrees F.

Step 2

Place flour, cornmeal and baking powder in a stand mixer fitted with the paddle attachment. Beat on low speed just until combined. Add butter and 1/2 cup yogurt. Beat until mixed, 2 to 3 minutes. Press the dough into the bottom and up the sides of a 9-inch tart pan with removable bottom. Top with parchment paper and pie weights.

Step 3

Bake the crust for 15 minutes. Remove the parchment and weights, and continue baking until the crust is golden brown and the bottom is set, about 10 minutes more. Let cool completely on a wire rack, about 30 minutes.

Step 4

Mix the remaining 1/2 cup yogurt, egg, Cheddar, mayonnaise, sugar, lemon zest and 1/2 teaspoon pepper in a medium bowl until smooth. Spread evenly in the cooled crust. Slice tomatoes 3/8-inch-thick and pat dry with paper towels. Arrange on top of the filling.

Step 5

Bake the tart until the filling is set, 25 to 30 minutes.

Step 6

Turn on the broiler and broil the tart until the top is lightly browned, 2 to 3 minutes. Let cool on a wire rack for 10 minutes. Remove the pan sides. Sprinkle the top with salt and the remaining 1/2 teaspoon pepper. Garnish with basil, if desired. Cut into 6 wedges.