In the bowl of a stand mixer, combine the flour, yeast, sugar, and salt. Whisk to combine then fit the stand mixer with a dough hook attachment.

In a 2-cup liquid measuring cup, whisk together the warm milk and egg until smooth. Add to the stand mixer bowl along with the butter.

Mix on low speed for 1 minute then scrape down the sides with a silicone spatula.

Increase to medium speed and beat for 5 minutes until a sticky cohesive dough forms and pulls away from the sides of the bowl.

Lightly grease a large bowl with olive oil. Transfer the dough to the bowl and cover tightly with plastic wrap. Let rise in a warm spot for 1-1 ½ hours until doubled in size.

Generously grease a 9×13-inch baking pan with ½ tbsp of softened butter. Punch down the dough to deflate it and turn out onto a lightly floured surface.

Lightly sprinkle the top of the dough with flour and use a bench scraper to divide it into 12 equal sized pieces. Weigh them; they should be around 63-65 g each.

Shape each piece into a smooth ball by folding the edges of the dough into the center and pinching to create a seam. Place the dough seam side down onto your work surface.

Cup your hand around the dough and swirl in a circle to create a sphere. Gently arrange and space out in the prepared baking pan.

Cover the pan loosely with plastic wrap or a large tea towel and let rise in a warm spot for 1 hour until puffy.

Preheat the oven to 375°F (190°C). Bake for 15-20 minutes until the tops are golden brown.

Meanwhile, in a small bowl, melt the remaining 2 ½ tbsp of butter. Mix in the garlic and parsley.

As soon as the rolls come out of the oven, brush them with the garlic butter and sprinkle the tops with flaky sea salt.