Roll the chilled pastry on a lightly floured surface into a very thin, roughly shaped circle, 14 inches in diameter.
Tip: If the dough is very firm, let it sit at room temperature about 10 minutes or tap the pastry all over with the rolling pin to flatten it a bit, then roll it out. You may not think the dough will be able to become 14 inches in diameter, but it will
Tip: If the dough feels too soft, fold it in half, transfer it to the pizza pan or rimmed baking sheet, unfold it, and refrigerate a few minutes.
Tip: Do not be concerned about rough edges of dough or if your circle is perfect. This is rustic. What’s important is that the dough is thin, thin, thin. The butter flakes melt during baking and the pockets of air that are formed make the pastry flaky.
Transfer the dough to the pizza pan or rimmed baking sheet.
Sprinkle the ground almonds and flour onto the center of the dough and distribute with your fingers into a thin powdery circle 10 to 11 inches in diameter.
Arrange plum halves cut side down in concentric circles on the nut layer.
Scatter the cold butter bits over the fruit, drizzle with lemon juice, and sprinkle evenly with 6 to 7 tablespoons of the sugar. Bring up edges of the pastry to cover the outer edge of peaches and press gently to adhere.
Brush the pastry with water and sprinkle with the remaining sugar.