In the bowl of a stand mixer, whisk together warm milk and honey. Sprinkle yeast over the top and let sit 5–8 minutes, until foamy.
Add the egg, softened butter, and salt. Mix until combined.
Add 3 ½ cups flour and knead with a dough hook for 6–8 minutes, until smooth and elastic. Add remaining flour only if the dough is too sticky.
Place dough in a greased bowl, cover, and let rise 1–1½ hours, until doubled in size.
Divide dough into 2 equal pieces. Roll each into a 12×7-inch rectangle. Spread 2 tablespoons butter over each and drizzle about 1 tablespoon honey over each rectangle.
Cut each rectangle into 8 long strips (starting on the long end). Roll each strip into a loose coil and place seam side down in a greased baking dish.
Cover and let rise 45–60 minutes, until puffy.
Brush rolls with melted butter and bake at 350°F for 18–22 minutes, until golden.
Brush with melted butter immediately after baking and sprinkle with flaky salt if desired.