1/4 cup lukewarm water
1 cup warm milk
3 tablespoons unsalted butter, melted and divided
2 whole eggs, lightly beaten
2 tablespoons granulated sugar
1 1/2 teaspoons fine salt
2 1/4 teaspoons (1 packet) instant yeast
4 1/2 cups bread flour
Flake sea salt, for sprinkling
Combine the water, milk, 1 tablespoon of the melted butter, eggs, sugar, salt and yeast in the bowl of a stand mixer. Add 2 cups of the flour and stir with a wooden spoon until the dough forms a rough, shaggy mass. Attach the dough hook to the mixer, turn to medium-low speed, and gradually add the remaining flour, kneading until a mass of dough begins to forms. Continue kneading on medium-high speed for 4 to 5 minutes until a soft, smooth ball of dough is formed. The dough should feel elastic and slightly tacky to the touch.
Lightly spray a large clean bowl with cooking spray and place the dough in the bowl. Cover the bowl lightly with plastic wrap. Let rise for about 45 minutes to 1 hour at room temperature or until the dough is big, puffy, and about doubled in size.
Spray a 13×9-inch baking pan with cooking spray. Gently deflate the dough. Use a bench scraper, knife, or pizza wheel to divide the dough into 15 equal pieces. Shape each piece into a ball and place in the prepared pan. Brush with the remaining 1 tablespoon of melted butter and sprinkle with flake sea salt. Lightly cover the dough with plastic wrap and let the rolls rise for 30 minutes, or until about doubled in size.
Preheat the oven to 375°F.
Bake the rolls for 20 minutes, or until golden brown. Brush with remaining 1 tablespoon melted butter. Serve warm. Store leftovers in a plastic bag for up to 3 days.