Preheat your oven to 350°F and lightly grease the base and sides of a 9x13 pan. Set it aside.

In a small saucepan, melt the butter, then mix in the minced garlic. Sauté for 1-2 minutes until aromatic, then take it off the heat and let it cool.

In the bowl of a stand mixer, combine the flour, sugar, parsley, yeast, and salt. Add in the warmed milk, egg, and garlic butter mixture. Knead on low speed using the dough hook until soft, smooth, and slightly tacky (about 10-12 minutes).

Divide the dough into 12 equal pieces (about 67 grams each). Roll each into a tight ball, ensuring the seam is pinched on the bottom. Place rolls in the prepared pan, cover, and let rise in a warm spot for 1-2 hours until doubled in size.

Once risen, brush the tops with beaten egg. Bake for 20-30 minutes until golden brown.

While the rolls bake, prepare garlic butter by melting butter, adding minced garlic, and cooking for 1-2 minutes. Stir in parsley off the heat. Brush the baked rolls with garlic butter and sprinkle with flaky sea salt.