Make chive butter: Combine butter, chives, and garlic in a bowl. Season with kosher salt and freshly ground black pepper. Set aside. (Makes ½ cup.)

Make biscuits: Whisk together flour, cornmeal, cornstarch, sugar, baking powder, and salt in a bowl. Cut frozen butter into flour mixture with a pastry cutter or two butter knives, until crumbs of varying sizes form. Add milk and stir to combine, then knead just until all the flour is incorporated and a dough forms, about 2 minutes. Turn dough out onto a lightly floured work surface. Fold in half 4 times to develop a stiff dough.

With a floured rolling pin, roll dough to a roughly 12- by 8-inch rectangle. Fold dough into thirds, as if you were folding a letter, then fold the two short ends of the dough toward the center. Wrap in plastic wrap and chill at least 40 minutes and up to 12 hours.

On a lightly floured work surface, roll dough to 1-inch thick and cut crosswise into thirds. Stack the three rectangles on top of one other and roll to 1-inch thick. Repeat 3 more times, leaving the final rectangle 1-inch thick. Chill 30 minutes.

Preheat oven to 475°F. Line a rimmed baking sheet with parchment paper. Place dough on a lightly floured work surface. Cut biscuits with a 3-inch round cutter; place on prepared baking sheet with biscuits slightly touching. Whisk together egg and 1 teaspoon water in a bowl. Brush on top of biscuits.

Bake, rotating the pan once, until golden brown and crisp on the outer edges, 15 to 17 minutes. Immediately brush with melted butter and sprinkle with flaky salt. Serve warm with chive butter alongside.