Hazelnut Butter Cake with Sea Salt Caramel

Preheat oven to 350 °F. Butter an 8"-diameter cake pan. Line with a parchment round; butter parchment. Dust pan with flour. Pulse hazelnuts and 1 tablespoon granulated sugar in a food processor until finely ground; set aside 2 tablespoons nut mixture. Whisk baking powder, salt, 1 cup flour, and remaining nut mixture in a medium bowl. Using an electric mixer on high speed, beat 1/2 cup butter and remaining granulated sugar in a large bowl until light and fluffy, about 3 minutes. Add eggs one at a time, beating to blend between additions. Reduce speed to low and mix in dry ingredients. Scrape batter into prepared pan, and sprinkle with reserved nut mixture and raw sugar. Bake until cake is golden brown and a tester inserted into the center of cake comes out clean, 40 –45 minutes. Transfer pan to a wire rack; let cake cool in pan before turning out. DO AHEAD: Cake can be baked 1 day ahead. Keep wrapped tightly at room temperature.