Make pastry: In a food processor, pulse flours and salt to mix. Add butter and whirl 3 seconds. Drizzle in 1/3 cup ice water, pulsing until mixture comes together in a shaggy ball but still has bits of butter showing. Form into a disk, wrap airtight, and chill at least 2 hours.
Make filling: Beat butter and 1/4 cup plus 2 tbsp. sugar in a bowl with a mixer on medium speed until light and fluffy. Switch to low speed, then blend in almonds, then egg, then flour, extracts, and salt until just combined.
Stir together cranberries, remaining 1/4 cup sugar, and 1 tbsp. water in a medium bowl. Set aside.
Roll pastry on a floured work surface into a 14-in. circle, turning pastry over and dusting with flour to prevent sticking. Trim edges, then transfer to a piece of parchment paper. Spread frangipane over pastry, leaving a 3-in. border. Top frangipane with cranberries.
Fold border of dough up and over cranberries, pleating dough as you go (berries will be uncovered in center). Press on pleats to seal, then transfer crostata on parchment to a rimmed baking sheet. Chill 30 minutes (otherwise pastry will ooze).
Preheat oven to 375°. Brush crust with egg wash. Bake crostata until deep golden brown, about 45 minutes. Loosen from pan with a spatula while still hot.
Make ahead: Pastry, up to 1 day, chilled. Frangipane, up to 2 days, chilled airtight; return to room temperature before using. Or bake crostata 2 days ahead; keep chilled, then rewarm at 350° for 15 minutes.
Note: Nutritional analysis is per serving.