Gather all ingredients.

Combine milk and 1 teaspoon of garlic in a small saucepan and cook over medium heat. Stir occasionally until just bubbling around the edges. Remove from heat, pour into a stand mixer bowl, and stir in sugar and butter. Let cool to 110°F–120°F (43°C–48°C), about 5–10 minutes.

Stir in yeast and let stand until foamy, about 10 minutes.

Add salt, egg yolk, 1 egg, and 2 cups of flour. Beat on low for 1 minute. Gradually add the remaining 1 3/4 cups of flour while beating on low until the dough just comes together. Increase speed to medium and knead for about 10 minutes until smooth and elastic.

Coat a large bowl with cooking spray. Transfer dough to the prepared bowl, turn to coat, and cover with plastic wrap. Let rise in a warm place until doubled in size, about 1 hour.

Heat 3 tablespoons of butter and the remaining garlic in a saucepan over medium-low heat until melted and fragrant, about 3 minutes. Transfer 1 1/2 tablespoons to a small bowl and set aside.

Lightly coat a 9x13-inch baking pan with cooking spray. Punch down dough and divide it into 20 pieces (about 1.4 ounces each). Form balls, dip in the butter-garlic mixture, and place seam-side down in the baking dish in 4 rows of 5. Cover with plastic wrap and let rise again, about 30–45 minutes.

Preheat the oven to 350°F (175°C).

Whisk together the remaining egg and 1 tablespoon of water. Brush tops of rolls with egg mixture.