Combine yeast with water and sugar. Give it a quick stir, and let it stand for 5 minutes to bubble (this is not necessary if using instant yeast).
In a bowl of a stand mixer, or in a large mixing bowl, combine the yeast mixture with oil, egg, flour, and salt. Knead using a stand mixer with a dough hook, or by hand, until you get a smooth and tacky dough ball.
On a lightly oiled surface, divide the dough into 9 balls (around 2oz/60g each).
Lightly grease an oven-proof ceramic baking dish (or a quarter baking sheet). And place the dough balls about half-inch apart. Cover with a towel or plastic/saran wrap and allow them to rise for at least 15 minutes. When I'm in a rush, I just let them rest for 15 minutes but if I have more time I let them rest for more until they double in size.
Preheat the oven to 375°F (190°C).
Remove the plastic wrap, and you can either bake the dinner rolls for 12-15 minutes without brushing them with anything (and brush the melted butter after they're baked and still warm). Or brush them with milk, egg wash, or butter before baking.