In a food processor, pulse 1 1/4 cups of the flour and the salt. Add 1 stick of the butter and pulse until it is the size of peas. Drizzle on the ice water and pulse until evenly moistened crumbs form; turn out onto a surface and form into a ball. Flatten into a disk, wrap in plastic and refrigerate until firm.
Preheat the oven to 375 degrees. Set a baking sheet on the bottom rack. In a bowl, toss the apples, lemon juice, sugar, the remaining 1/4 cup of flour and the cinnamon.
Spread the apple filling in an 8×11-inch baking dish and dot with the remaining 1 tablespoon of cubed butter. On a floured surface, roll out the dough 1/8-inch thick and cut it into 2-inch squares or desired shapes (I used a 2-inch star). Arrange the squares of dough in a patchwork pattern over the apples, pressing them onto the edge of the baking dish and leaving a few openings for steam to escape.
Bake the pandowdy in the center of the oven for 1 hour, until the crust is golden. Let the pandowdy cool for at least 4 hours before serving with a big scoop of vanilla ice cream!