Separate your eggs first. Crack both eggs, setting aside one whole yolk for the butter dough and reserving the white in a separate small bowl for the egg wash later.

Proof the yeast. In a measuring cup or bowl, combine the warm whole milk, instant yeast, 1 tablespoon of sugar, and 1 tablespoon of honey. Stir gently and let sit for 5–10 minutes, until foamy on top.

Build the butter dough. In a mixing bowl, combine 1 cup of the flour, the melted butter, 1 teaspoon of coarse salt, the remaining 1 tablespoon of sugar, the whole egg, and the reserved egg yolk. Begin kneading by hand. When the dough starts to stick to your hands, rub 1 tablespoon of olive oil into your hands and continue kneading directly with your hands until the oil is fully worked in. If the dough is still sticky, rub 1 teaspoon of olive oil into your hands and knead again. Do not add extra flour or water to compensate for stickiness. Continue until the dough comes together into a smooth ball.

Build the yeast dough. In a separate bowl, combine the remaining 2 cups of flour with the remaining 1 teaspoon of coarse salt. Pour in the proofed yeast mixture and mix until just incorporated. This dough does not need a full knead, just full combination.

Combine and knead. Combine both doughs into one bowl and knead together for about 10 minutes. The dough may look uneven or separated at first. Keep kneading; it will come together into a smooth, cohesive dough.

First rest. Cover the combined dough with a clean towel or plastic wrap and let it rest until slightly puffed.

Second knead and rest. Knead the dough again for 5–10 minutes, then cover and let rest a second time, until it feels fully incorporated and elastic.

Shape the rolls. Divide the dough into 12–16 equal balls for standard dinner-roll size (15 is the sweet spot), or shape larger if making hamburger buns. Place in a greased baking dish or on a lined sheet pan, leaving room to expand.

Final proof. Cover the shaped rolls loosely and let rise until doubled in size.

Preheat and egg wash. Preheat the oven to 350°F. Whip the reserved egg white until bubbles form; you do not need stiff peaks. Brush generously over the tops, sides, and creases of every roll.

Bake. Bake for 22–26 minutes, until the tops are deeply golden. Baking time will vary depending on your oven and even the season, so watch color rather than the clock alone.

Make the honey butter. While the rolls bake, combine the butter, 2% milk, and honey in a microwave-safe bowl. Microwave in 20–30 second bursts, stirring until smooth. Have it ready before the rolls come out of the oven.

Double-coat with honey butter. As soon as the rolls come out of the oven, brush the honey butter mixture generously over the tops and into the creases of every roll. Wait about 30 seconds, then brush a second coat over the top. Do not skip the second coat.