Lightly butter the bottom and sides of a 9x13 baking pan and set it aside.

In a small pot, melt the butter over low heat and add the minced garlic. Cook for 1-2 minutes until fragrant, then remove from heat and let it cool.

In a stand mixing bowl, combine the flour, parsley, sugar, instant yeast, and salt. Stir to blend the dry ingredients.

Pour in the warmed milk, egg, and the cooled garlic butter. Use a dough hook to knead on low speed for 10-12 minutes until the dough is smooth and soft yet tacky.

If the dough is too sticky, add flour one tablespoon at a time until the desired consistency is reached.

Divide the kneaded dough into 12 equal portions, each weighing about 67 grams. Shape each piece into a smooth ball.

Place the shaped dough balls into the prepared baking pan, cover with plastic wrap or a kitchen towel, and let them rise until doubled in size, about 1-2 hours.

Preheat your oven to 350°F (180°C) while the rolls are rising.

Once the rolls have risen, brush the tops with the beaten egg wash.

Bake for 20-30 minutes until golden brown and sound hollow when tapped.

While the rolls bake, prepare the garlic butter topping by melting butter in a small saucepan, adding minced garlic, and cooking for 1-2 minutes. Stir in parsley.

Immediately brush the hot rolls with the garlic butter and sprinkle with flaky sea salt before serving warm.