Warm the milk: Heat the milk until it reaches about 110°F, warm but not hot to the touch. Stir in the yeast and a pinch of the sugar, then let it sit for 5 to 10 minutes until foamy on top.

Combine dry ingredients: In a large bowl, whisk together the flour, remaining sugar, and salt. This spreads the salt evenly so it doesn't slow down the yeast in one spot.

Mix the dough: Add the foamy yeast mixture, egg, and 2 tablespoons of the softened butter to the dry ingredients. Stir until a shaggy, sticky dough forms.

Knead until smooth: Turn the dough onto a floured surface and knead for 8 to 10 minutes, adding small amounts of flour as needed. The dough is ready when it's smooth, elastic, and only slightly tacky.

First rise: Place the dough in a greased bowl, cover with a towel or plastic wrap, and set it in a warm spot. Let it rise for about 1 hour, until it has doubled in size.

Shape the rolls: Punch down the risen dough to release the air, then divide it into 12 equal pieces. Roll each piece into a tight, smooth ball using your palm against the counter.

Arrange in the pan: Place the shaped rolls close together in a greased 9x13-inch baking dish so their edges touch. This helps them rise into each other for soft, tearable sides.

Second rise: Cover the pan loosely and let the rolls rise again for 30 to 45 minutes, until they look puffy and have grown noticeably in size.

Make the garlic butter: While the rolls rise, melt the remaining 4 tablespoons of butter and stir in the minced garlic and chopped parsley. Set aside half for after baking.

Bake the rolls: Preheat the oven to 375°F. Brush the rolls with half of the garlic butter, then bake for 18 to 22 minutes, until the tops turn deep golden brown.

Brush and finish: As soon as the rolls come out of the oven, brush them with the remaining garlic butter and sprinkle with flaky sea salt. Let them cool for 5 minutes before serving so the butter soaks in.