Cheddar Cheese Buns

In a small saucepan over medium heat, warm the milk until small bubbles appear along the edges of the pan. Remove from the heat. Add the 1/3 cup sugar, the 4 Tbs. butter and the salt; stir to dissolve the sugar. Let cool to lukewarm, about 105°F.

Meanwhile, in a small bowl, sprinkle the yeast over the lukewarm water, stir in the 1 tsp. sugar and let stand until foamy, about 5 minutes. Transfer the yeast mixture to a large bowl and add the lukewarm milk mixture, the egg and cheese. Using a wooden spoon, beat until smooth. Add 3 cups of the flour and beat until well mixed. Continue adding the flour, about
1/2 cup at a time and beating well after each addition, until the dough is smooth and comes away from the sides of the bowl, 10 to 12 minutes. (The dough can also be made with a stand mixer fitted with a dough hook; it will take 6 to 8 minutes.)

Turn the dough out onto a floured board, cover with the bowl and let rest for 5 minutes. Then knead until the dough is smooth and elastic and holds the imprint of a finger when poked, 7 to 9 minutes. Shape into a ball. Butter a clean bowl, place the dough in it and turn to coat. Cover with a damp kitchen towel, set in a warm area away from drafts and let the dough rise until doubled in volume, about 1 hour.

Grease 3 baking sheets with solid vegetable shortening or nonstick cooking spray. Using your hands, pinch off a tennis-ball-size piece of dough, shape into a ball and place on the prepared sheet. Repeat with the remaining dough, spacing the buns about 2 inches apart. Flatten each bun with your fingers, brush the tops with the melted butter, and sprinkle about 1 tsp. onion over each. Cover with a damp kitchen towel and let rise a second time until doubled in volume, 30 to 40 minutes.

Preheat an oven to 375°F.

Bake until the tops of the buns are browned and the bottoms sound hollow when tapped, 25 to 30 minutes. Remove from the oven and serve warm.