Preheat the oven to 400?F.
In a large bowl, blend the flour, baking powder and salt. Add the butter and blend with a fork or pastry cutter (or rub with your fingers) until well blended, with pieces no bigger than a pea. Add the milk and stir by hand just until you have a soft dough.
Divide the dough in half (with one half just 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. Roughly chop the tomatoes (I cut them in half, then each half in 6 or 8) and put them in a colander on a plate or in the sink; let drain, swishing the tomatoes around with your hand to loosen any seeds and release more liquid, for 10 minutes or so.
Arrange half of the tomatoes in the crust and sprinkle 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 roughly to seal—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 crust with a bit of milk or cream.
Bake for 30-35 minutes, until the pie is deep golden. Serve warm, or cool to room temperature. Serves 8.