In the bowl of a stand mixer, combine the all-purpose flour, instant yeast, and salt. Add the warm milk, 3 tablespoons of honey, 3 large eggs, and 6 tablespoons of softened salted butter. Using the dough hook, mix everything together until the flour is completely incorporated, about 4–5 minutes. If the dough is too sticky, add up to 1/4 cup of flour at a time until it becomes soft and workable. Cover the bowl with plastic wrap and let the dough sit at room temperature for at least 15 minutes, or up to 1 hour. I find allowing the dough to rest longer gives the rolls a softer texture.
While the dough rests, prepare the sage honey butter. In a skillet over medium heat, fry the sage leaves with 1 tablespoon of softened salted butter until crispy, about 1–2 minutes. Remove the fried sage leaves from the pan and chop them finely. In a small bowl, mix together 6 tablespoons of softened salted butter and 3 tablespoons of honey, then stir in the chopped fried sage and a generous pinch of flaky sea salt. This aromatic butter is what gives the rolls their unique flavor—I like to taste the sage butter at this stage to make sure it's well-seasoned.
Preheat your oven to 350°F (175°C). Line a 9×9 inch baking dish with parchment paper. Once the dough has rested, punch it down to release excess air and divide it in half. On a lightly floured surface, roll out each half into a 12-inch square, about 1/4-inch thick. Brush each square with the sage honey butter from Step 2, reserving any leftover butter for serving. Cut each square into 6 strips and roll each strip into a coil. Arrange the coils seam side down in the prepared baking dish. If you want perfectly even coils, try to cut the strips as evenly as possible.
In a small bowl, beat together the egg yolk with 1 tablespoon of water. Brush the tops of the dough coils with the egg wash to help them brown beautifully in the oven. Cover the baking dish with a clean kitchen towel or plastic wrap and let the rolls rise for 30 minutes, until they appear puffy.
Bake the rolls in the preheated oven for 22–25 minutes, or until they are golden brown on top. Remove from the oven and immediately brush the warm rolls with any remaining sage honey butter from Step 2. Pull them apart to serve and finish with a light sprinkle of flaky sea salt, if desired. For extra flavor, I like to serve these rolls warm so the honey butter soaks in perfectly.