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1
Whisk together flour, baking powder, and 3/4 teaspoon salt in a bowl, then blend in 3/4 stick cold butter with your fingertips or a pastry blender until it resembles coarse meal.
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2
Add milk, stirring until mixture just forms a dough, then gather into a ball.
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3
Divide dough in half and roll out 1 piece between sheets of plastic wrap into a 12-inch round (1/8 inch thick).
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4
Remove top sheet of plastic wrap, then lift dough using bottom sheet of plastic wrap and invert into a 9-inch glass pie plate, patting with your fingers to fit (there will be just enough dough to line plate without an overhang).
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5
Discard plastic wrap.
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6
Preheat oven to 400F.
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7
Whisk together mayonnaise and lemon juice.
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8
Arrange half of tomatoes in crust, overlapping, and sprinkle with half of corn, 1 tablespoon basil, 1/2 tablespoon chives, 1/8 teaspoon pepper, and 1/2 teaspoon salt.
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9
Repeat layering with remaining tomatoes, corn, basil, chives, pepper, and salt, then sprinkle with 1 cup cheese.
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10
Pour lemon mayonnaise over filling and sprinkle with remaining cheese.
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11
Roll out remaining piece of dough into a 12-inch round in same manner, then fit over filling, folding overhang under edge of bottom crust and pinching edge to seal.
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12
Cut 4 steam vents in top crust and brush crust with 2 teaspoons melted butter.
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13
Bake pie in middle of oven until crust is golden and filling is bubbling, 30 to 35 minutes, then cool on a rack.
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14
Serve warm or at room temperature.
