In a small saucepan, melt the unsalted butter with minced garlic over medium heat, stirring until fragrant, about 2-3 minutes. Allow to cool slightly.

In a stand mixer bowl, combine flour, parsley, granulated sugar, yeast, and salt. Use the paddle attachment on low speed to mix.

Add warmed milk, egg, and cooled garlic butter to the dry mixture. Knead on low speed for 10-12 minutes until smooth and slightly tacky.

Transfer the dough to a floured surface, divide into 12 equal pieces, and shape into balls. Place in a greased baking pan.

Cover the pan and let the rolls rise in a warm place until doubled in size, about 1-2 hours.

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

Immediately brush tops with melted garlic butter after baking and sprinkle with flaky sea salt if desired.