Lightly butter the bottom and sides of a 9×13 pan and set it aside.

In a small pot, melt the butter and add the minced garlic. Cook for 1-2 minutes or until the garlic is fragrant. Take off the heat and cool while you measure the other ingredients.

In a stand mixing bowl, combine the flour, parsley, sugar, yeast, and salt. Then add the warmed milk, egg, and garlic butter from above. Knead on low speed with the dough hook until the dough looks smooth and feels soft and tacky, about 10-12 minutes.

Cut the kneaded dough into 12 equal portions. Shape each piece of dough into a smooth ball. Pinch the bottom of the roll where the seam comes together to keep it tight. Place the shaped dough balls into the prepared baking pan. Cover the top with plastic wrap or a clean kitchen towel and set them in a warm place to rise until doubled in size, about 1-2 hours.

Preheat the oven to 350°F (180°C).

Brush the tops of the rolls with the beaten egg wash. Then bake the dinner rolls for 20-30 minutes, or until the tops are golden brown.

While the rolls are baking, make the garlic butter. Melt the butter in a pot and add the minced garlic. Cook for 1-2 minutes until the garlic is fragrant. Remove it from the heat and stir in the parsley. When the rolls come out of the oven, immediately brush them with the garlic butter. Sprinkle with flaky sea salt if desired, and serve warm!