In a large mixing bowl, combine the flour, sugar, and fine sea salt. Add the cold, cubed butter and use your fingertips or a pastry cutter to work it into the flour until the mixture resembles coarse crumbs with some pea-sized butter pieces remaining.

Make a well in the center and add the 3 egg yolks and vanilla extract. Use a fork to gradually incorporate the dry ingredients until a shaggy dough forms. Then, gently knead by hand just until the dough comes together into a smooth ball. Do not overwork.

Flatten the dough into a disc, wrap tightly in plastic wrap, and refrigerate for at least 1 hour (or up to 2 days).

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper. On a lightly floured surface, roll the dough to about 1/4-inch thickness. Use a 2.5-inch round cookie cutter to cut out biscuits. Re-roll scraps once.

Place rounds on prepared sheets, spacing 1 inch apart. Brush lightly with egg wash. Use the back of a fork to create a crosshatch pattern, then sprinkle each with a tiny pinch of coarse sea salt. Bake for 15-18 minutes, rotating halfway, until edges are golden and centers are set.

Let biscuits cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely. They will crisp up as they cool.