Warm the milk and water together to about 100–110°F (warm to the touch). In a large mixing bowl or the bowl of a stand mixer, combine the warm liquid, sugar and instant yeast. Stir and let sit 5 minutes until foamy.

Combine dry ingredients

Add the flour and fine sea salt to the bowl with the yeast mixture. Add the softened butter cubes and the egg.

Mix and knead

Using a stand mixer with a dough hook on low-medium speed, mix until the dough comes together, about 3–4 minutes. Increase speed slightly and knead 5–7 minutes until the dough is smooth, slightly tacky but not sticky. If mixing by hand, turn out onto a lightly floured surface and knead 8–10 minutes.

First rise

Shape dough into a ball, place in a lightly oiled bowl, cover with plastic wrap or a damp towel, and let rise in a warm draft-free place until doubled, about 1–1.5 hours.

Shaping & Filling

Prepare workspace

Turn the risen dough out onto a lightly floured surface and gently deflate. Divide dough into 10 equal pieces (about 65–75 g each) for individual rolls or shape as desired for one longer loaf.

Roll and butter

Flatten each piece into a small rectangle with your hands or a rolling pin (about 4 x 3 inches). Brush the surface lightly with about 1/2 teaspoon of the melted butter from the filling ingredients (reserve remaining). Optionally sprinkle a scant pinch of the granulated sugar on each, then fold or roll tightly into a classic roll shape, tucking ends underneath so the seam is on the bottom.

Arrange for second rise

Place shaped rolls seam-side down into a greased 9x13-inch baking pan or onto a parchment-lined baking sheet spaced about 1 inch apart. Cover loosely with plastic wrap or a towel and let rise until nearly doubled, about 30–45 minutes.

Bake & Finish

Preheat oven

While rolls are undergoing their second rise, preheat the oven to 375°F (190°C). Position a rack in the center of the oven.

Brush and salt

Just before baking, brush the tops of the rolls with the remaining melted butter (use the 1 tbsp from 'for brushing' plus any leftover from the filling measurement as needed). Sprinkle the coarse sea salt evenly over the tops (about 1/4 teaspoon per roll, adjusting to taste). If using, sprinkle a light dusting of the tablespoon of granulated sugar across the pan for a faint sweet-salty contrast.

Bake

Bake in the preheated oven for 15–20 minutes, or until the tops are deep golden brown and internal temperature reaches about 190°F (88°C). If baking a single loaf, bake 25–30 minutes.

Cool slightly

Remove from oven and let the rolls cool in the pan for 5–7 minutes. If desired, brush once more lightly with melted butter for extra sheen and softness.

Serve

Transfer rolls to a wire rack and serve warm. The flaky sea salt on top should provide a bright contrast to the rich buttery crumb.