Unroll 1 pie dough into a round. Arrange three 4 1/4-inch nonstick tartlet pans on the dough and use a paring knife to cut a circle of dough around each that is about 1/2 inch larger than the pan; these don't have to be perfect, but you want to make sure you cut enough excess dough to fill the pan and up the sides. Press the dough evenly into each pan; if any excess dough goes over the top, simply use the top edge of the tartlet pan to cut it away. Use a fork to dock the bottom of the pie crusts. Repeat this process with 3 more tartlet pans and the remaining pie dough. Place the 6 tartlet pans on a baking sheet and put in the freezer for 10 minutes.
In a medium bowl, toss together the cherry tomatoes, garlic, salt and pepper. Let the tomatoes sit for 10 to 15 minutes for the flavors to combine.
Bake the crusts until the dough is cooked part of the way through without any color and bubbles form on the bottom and sides, about 6 minutes. Let cool slightly.
To each tartlet, add about 3 tablespoons of grated Cheddar and spread evenly over the bottom. Top the cheese in each with 8 tomato halves cut-side up, making sure to get some garlic with each tomato. Bake until the crusts are golden brown, the cheese is bubbling and the tomatoes are softened but have not burst, about 30 minutes. Let cool until cool enough to handle, 5 to 10 minutes. Remove the tartlets from the tart pans and garnish with small basil leaves.
These tartlets can be stored in the refrigerator after they have cooled completely and reheated in the oven the next day for great leftovers!