Combine the flour, baking powder, and salt in a large mixing bowl.
Add the butter and pinch it into the flour until it is all in pea-sized bits.
Add the milk and mix with a spoon or by hand until the dough comes together. If you need to add more milk, do so.
Smash half of this dough into the bottom of a pie plate (it will be about a half-inch thick). According to Ann, it doesn't matter if it comes up the side, just the bottom. Though Colwin asks you to roll the dough out, which is fine, too.
Heat your oven to 400˚F.
Slice the tomatoes and layer them on top of the dough.
Mix the mayo and lemon juice, and pour this over the tomatoes. (If you wish, add basil here.)
Top it all with the cheddar cheese. Fashion the remaining dough into a top and spread it over the pie. Try to cover the entire pie but don't worry overly about this; it's a biscuit crust.
Bake for 30 minutes or until the crust is golden brown and cooked through.