Preheat the oven to 400F.
In a large bowl, combine the flour, baking powder and salt. Add the butter and blend it with a fork or rub it in with your fingers. Add the milk and stir by hand just until you have a soft dough.
Divide the dough in half (I make one half slightly larger than the other) and roll the larger piece on a lightly floured countertop to about an 11-inch round; transfer to a pie plate and gently fit it inside without stretching.
In a small bowl, whisk together the mayonnaise, lemon juice and garlic. Slice the tomatoes about 1/4 inch thick; if you like, salt them and let them drain in a colander or on paper towels for 20 minutes or so to get rid of excess liquid.
Arrange half of the tomatoes in the bottom crust, overlapping them, and top with half the corn, half the basil and chives, a sprinkle of salt and pepper and half the grated cheese. Repeat with remaining tomatoes, corn, basil, chives, salt and pepper. Pour the lemony mayonnaise overtop and sprinkle with the remaining cheese.
Roll out the other piece of dough into a 10-inch circle and fit it over the filling, folding the overhang under edge of bottom crust (or vice versa) and pinching/crimping to seal around the edge, or press it all around with a fork—it doesn’t have to be perfect. Cut a couple vents in the top crust to help let some steam escape and if you like, brush the crust with a bit of milk, cream or melted butter.
Bake for 30-35 minutes, until the pie is deep golden. Serve warm, or cool to room temperature. Serves 8.