Salted Butter and Chocolate Chunk Shortbread

Ingredients

Check off items as you prep or cook them

1 cup plus 2 tablespoons (2¼ sticks) cold salted butter, cut into ½-inch pieces
½ cup granulated sugar
¼ cup (packed) light brown sugar
1 teaspoon vanilla extract
2¼ cups all-purpose flour
6 ounces semisweet or bittersweet dark chocolate, chopped (but not too fine, you want chunks, not thin shards of chocolate)
1 large egg, beaten to blend
Demerara sugar (for rolling)
Flaky sea salt