Combine warm water, yeast, and sugar in the bowl of a stand mixer. Whisk to blend and set aside for 8 minutes, or until yeast has activated and is very frothy.
Add 3 cups flour, 3 tablespoons butter, egg, and salt to the bowl. With the dough hook fitted, turn mixer on medium speed until the dough comes together into a ball. Turn speed down to a "2" (medium-low) and continue kneading for 3 minutes, until dough ball is smooth. If your dough is too wet, add a little bit more flour until the dough ball forms.
Cover bowl with a tea towel and set aside to rise until doubled in size, 1 to 1 1/2 hours.
Scrape dough out of the bowl and divide into 12 pieces. Roll each piece into a smooth ball.
Spray a 9x13-inch baking dish with cooking spray. Arrange dough balls in the baking dish. Cover again with the tea towel and set aside until well risen and puffy, 30 to 40 more minutes.
Preheat the oven to 350 degrees F (175 degrees C).
Bake rolls in the preheated oven until golden brown and baked through, 20 to 25 minutes.
Remove from the oven and allow to cool a few minutes. Brush remaining tablespoon softened butter over the top of the warm rolls, allowing the butter to soak in.
Nutritional Facts
Per 12 servings
Calories: 172
Carbohydrate: 28g
Fat: 5g
Fiber: 1g
Protein: 4g
Sugar: 4g
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