Place flour, salt, and butter in a large bowl. Using a pastry blender or 2 knives, cut the butter into the flour until you have a fairly uniformly coarse mixture. From the glass of ice water, measure 6 tablespoons of water and sprinkle over the crumbly dough then stir with a fork. If the mixture seems dry, add the remaining 2 tablespoons of water. Your mixture will look crumbly, but when you pinch a small amount it will clump together.

Dump crumbly dough onto counter, then push and pat together into a thick round. If the dough isn’t coming together, sprinkle additional ice water 1 tablespoon at a time and keep pressing and forming. Cut the round into 3 pieces, then shape each into disks about 1-inch thick. Wrap each in parchment or plastic wrap and let rest in the refrigerator for at least 45 minutes (or up to 2 days) before rolling. Alternatively, you can freeze the dough disks at this time.

Preheat oven to 400°F. Place 1 pastry disk on a sheet of parchment or lightly floured surface and using a lightly floured rolling pin (or wine bottle), roll out into a thin, roundish shape approximately 12 inches in diameter. Transfer the pastry-on-parchment to a baking sheet (parchment-lined if you didn't roll on parchment), spoon on the cherries (keep an eye out for stray pits), dot with butter, sprinkle with 1 tablespoon sugar, and spritz with lemon. Fold edges of pastry up and over the cherries. Brush the exposed pastry with milk or cream, then sprinkle with sugar. Bake until golden brown, approximately 30 minutes. Let cool on rack, then enjoy with a scoop of ice cream.