Roast the hazelnuts. Spread them in a single layer on a baking sheet and bake at 375°F for 10–12 minutes until fragrant and lightly browned. Let cool slightly, then rub between a kitchen towel to remove most of the skins. Roughly chop — you want bits, not powder.
Make the dough. In a bowl, whisk together flour, salt, and sugar. Cut in cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs with some pea-sized pieces remaining. Sprinkle ice water over the top, one tablespoon at a time, mixing gently just until the dough comes together when pressed between your fingers. Form into a disk, wrap tightly, and chill for 30 minutes.
Prepare the filling. Toss raspberries with sugar, lemon juice, cornstarch, vanilla extract, and chopped hazelnuts in a medium bowl. Set aside while you roll out the dough.
Roll out the galette. On a lightly floured surface, roll your chilled dough into an 11- to 12-inch circle — it doesn't have to be perfect. Transfer to a parchment-lined baking sheet. Leave a 1½-inch border around the edge.
Assemble. Spoon filling onto the center of the dough, leaving that border clear. Fold the edges up and over the fruit, pleating as you go. Don't worry if some juice seeps out — it'll caramelize beautifully in the oven. Brush the crust with egg wash and sprinkle with coarse sugar if using.
Bake. Bake at 400°F for 35–40 minutes until the crust is golden brown and the filling is bubbling around the edges. Transfer to a wire rack and let cool for 15 minutes before slicing.
Serve warm or at room temperature with whipped cream, crème fraîche, or a scoop of vanilla ice cream on top.
