Lightly butter the bottom and sides of a 9x13 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. Remove from heat and cool.

In a stand mixer, combine the flour, parsley, sugar, yeast, and salt. Add the warmed milk, egg, and cooled garlic butter.

Knead on low speed with the dough hook for about 10-12 minutes until smooth and soft. Add more flour if the dough is too sticky.

Cut the kneaded dough into 12 equal portions (about 67 grams each) and shape into smooth balls. Pinch the seams together and place in the prepared pan.

Cover with plastic wrap or a clean kitchen towel and let rise in a warm place 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. Bake for 20-30 minutes or until golden brown.

While the rolls bake, prepare the garlic butter. Melt the remaining butter, add minced garlic, and cook for 1-2 minutes until fragrant. Stir in parsley.

Brush the baked rolls with garlic butter as soon as they come out of the oven, and sprinkle with flaky sea salt if desired.