Cheddar Cheese Buns

Ingredients

• 1 1/2 cups milk
• 1/3 cup plus 1 tsp. sugar
• 4 Tbs. (1/2 stick) unsalted butter
• 1 Tbs. salt
• 5 tsp. (2 packages) active dry yeast
• 1/2 cup lukewarm (105°F) water
• 1 egg, lightly beaten
• 1 1/2 cups shredded sharp cheddar cheese
• About 6 cups all-purpose flour
• About 3 Tbs. unsalted butter, melted
• 1 yellow onion, finely chopped