In your stand mixer bowl, mix together 1¼ cup of flour, the salt, and the yeast. Set this aside.
3¾ Cups Flour, 2¼ Tsp Active Dry Yeast, ½ Tsp Salt
In the saucepan, heat up the milk, sugar, and butter on medium until it reaches 125℉. Try not to let it get any hotter or it can kill the yeast and leave your dough flat and sad.
1 Cup Whole Milk, 3 Tbsp Sugar, ⅓ Cup Butter
Add the milk mixture to the mixing bowl, and add the egg. Beat this with the beater attachment on low for about 30 seconds to start working it together. Scrape down the sides of the bowl and continue mixing on high for 2-3 minutes. Gradually add the remaining flour.
1 Egg, 3¾ Cups Flour
Switch to the dough hook attachment and knead the dough with it for 4-5 minutes, until it's smooth and elastic. If it's still sticky, add a bit more flour, a tablespoon at a time, until it doesn't stick to you when you poke with a finger.
Using some oil, lightly grease your mixing bowl. Shape the dough into a ball, put it in the bowl, and turn it to coat the dough ball with oil. Cover the bowl with a clean towel and place it in a warm place to rise for at least an hour, aiming for it to double in size.
When the dough is nearly risen, make your garlic butter by mixing the butter, parsley, chives, and garlic in another bowl, until it's well combined. Set this aside.
¾ Cup Butter, 3 Tbsp Parsley, 3 Tbsp Chives, 8 Cloves Garlic
Punch down the dough and turn it out onto a lightly floured surface. You don't need to knead it, just cover it and let it rest for another 10 minutes. While you're waiting, grease your baking dish.
Using your rolling pin, roll the dough out. You want it to be a rectangle roughly 8"x10", and about even thickness throughout.
Spread about ¾ of the butter mixture evenly across the surface of the dough. Mix up your cheeses and spread them evenly on top of the butter, leaving about an inch along one of the long sides of the dough un-cheesed.
1 Cup Shredded Mozzarella, 1 Cup Shredded Cheddar, 1 Cup Grated Parmesan
Starting at the long edge with cheese on it, start rolling up the dough, keeping it as tight as you can. When rolled up, press the seam closed with your fingers.
Cut the ends of the dough log off for even sizing, then cut the remainder into 12 equally-sized discs of filled dough spiral. You can discard (or bake separate) the remains, they just don't rise right if you include them with the rest.
Arrange the 12 spirals in your baking dish. Cover this and let it rise again for 30-45 minutes. While they're rising, preheat your oven to 375℉.
Bake your rolls for 25 minutes. When they're nicely golden, remove them from the oven and let them cool for about 10 minutes.
Melt the remaining garlic butter mixture and drizzle or brush it over the top of the rolls, then serve warm and enjoy!