Preheat the oven to 400°F. In a large bowl, combine warm water, olive oil, white sugar, and yeast. Allow the mixture to sit for about 8-10 minutes until the yeast becomes bubbly.
1 cup warm water, ⅓ cup olive oil, ¼ cup white sugar, 2 Tablespoons active dry yeast
Stir in the beaten egg, softened butter, and salt.
1 egg, 1 Tablespoon butter, 1 teaspoon salt
Using a stand mixer with a dough hook attachment or your hands, mix in the all-purpose flour one cup at a time until you have a soft dough that isn't overly sticky. We used about 4 cups of flour, but it may take you anywhere from 3-4.
3 to 4 cups all-purpose flour
Sprinkle a bit of flour on top of your dough, then knead it by hand for 10 minutes (or 5 minutes with a stand mixer).
Divide the dough into 18 pieces and shape them into balls.
Place the dough balls on a greased 10 by 15-inch pan and cover them with parchment paper and a kitchen towel.
Let the dough rise for 10 minutes in a warm place, but if you have more time, you can let them rise for up to 30 minutes.
Lightly brush the rolls with milk and bake them on the middle rack in the oven for 15-17 minutes or until they're just browned.
⅛ cup milk
For the finishing touch, top the rolls with melted butter or garlic butter immediately after baking.