In the bowl of a stand mixer, combine the flour, yeast, parmesan, and salt. Add the warm milk, honey, 2 eggs, and 2 tablespoons butter. Use the dough hook to mix until the flour is incorporated, about 4-5 minutes.

If the dough is sticky, add the remaining 1/4 cup of flour. Cover the bowl and let sit at room temperature for 30 minutes to 1 hour.

In a skillet, heat 2 tablespoons butter, garlic, and sage over medium heat until browned and sage is crisp, about 3-4 minutes.

Let cool, then mash the garlic and chop the sage. Mix with 4 tablespoons butter.

Butter a 9x5-inch loaf pan and preheat the oven to 450°F.

When the dough has doubled, turn it out, punch down, and shape it into a rectangle (12 x 18 inches). Spread sage butter, roll into a log, and cut into 8 rolls.

Pinch the ends to seal and arrange in the pan. Cover and let rise for 15-20 minutes.

Brush with beaten egg and bake for 20 minutes. Reduce temperature to 350°F and bake another 25-30 minutes.

Serve warm with additional butter.