For the pastry:
2 1/2 cups all-purpose flour
1 teaspoon salt
2 sticks (1 cup) unsalted butter, cold, cut into small chunks
4 tablespoons ice water, plus more if needed
For the filling:
1/2 cup brown sugar
2 teaspoons ground cinnamon
1 tablespoon all-purpose flour
1 large egg, whisked with a tablespoon of water, to brush the pastries with
For the glaze:
3/4 cup powdered sugar, sifted
4 teaspoons milk, plus more as needed
1/2 teaspoon ground cinnamon
1/4 teaspoon vanilla extract