Lightly butter a 9x13 baking pan. In a small saucepan, melt 4.5 tablespoons of butter with 2 tablespoons of minced garlic. Cook for 1-2 minutes until fragrant, then set aside to cool.

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

Knead on low speed using a dough hook for 10-12 minutes until the dough is smooth, soft, and slightly tacky.

Divide the dough into 12 equal portions (approx. 67g each). Shape each into a smooth ball by cupping your hand and rotating on the counter, then place into the prepared baking pan.

Cover with plastic wrap and let rise in a warm place for 1-2 hours until doubled in size.

Preheat oven to 350°F. Brush the rolls with beaten egg wash and bake for 20-30 minutes until golden brown.

While baking, prepare the final garlic butter by melting 2 tablespoons butter with 1 tablespoon garlic and 1 tablespoon parsley. Brush over hot rolls immediately after removing from the oven and sprinkle with flaky sea salt.