Mix milk, brown sugar, and white sugar together in a microwave-safe bowl. Microwave until warm, 40 to 50 seconds. Stir in yeast.
Whisk 6 tablespoons butter and eggs in a separate bowl. Whisk into the milk mixture until just combined, 30 to 60 seconds. Stir in flour, 1/2 cup at a time, mixing well after each addition until dough is smooth and still wet.
Place dough in a greased bowl. Loosely cover and let rise in a warm, dry place until doubled in volume, about 1 hour.
Transfer dough to a floured work surface. Drizzle with honey and salt. Fold in half and repeat the honey-salt drizzle. Repeat folding and drizzling, 5 to 6 times.
Roll dough into a rectangle about 1/2-inch in thickness. Cut into 12 equal pieces using a pizza cutter. Place rolls on lightly greased 9x13-inch baking pans or on lightly greased baking sheets. Cover rolls with a light cloth and let rise again until doubled in volume, 45 minutes to 1 hour.
Preheat oven to 350 degrees F (175 degrees C).
Bake rolls in the preheated oven until tops begin to brown, 11 to 14 minutes. Brush the remaining 1/2 tablespoon butter and some honey over the rolls right after removing from the oven.