Put flour, baking powder and 1/2 teaspoon salt in a bowl and stir with a fork. Drop in butter and cut into flour until pieces are the size of small peas. Pour in milk and stir until dough hasn't quite come together. Dump it on the counter and knead to work in dry flour.
3Divide the dough in half. Roll one half out until if is large enough to line a 10-inch pie plate.
Mix the tomatoes with the basil and half the cheddar and some salt. Pat this out evenly in the pastry. Spread the tomatoes with the mayonnaise and spread the rest of the cheese on top.
5Roll out the rest of the dough, and top the pie. Trim the top and bottom crusts back to the rim. Seal edges.
6Bake pie until golden, 20 to 25 minutes. Let cool for a while before serving. It should be warm, not hot.