Place tomato sauce in a small saucepan over medium-low heat and bring to a simmer.
Melt butter with olive oil in a large saucepan over medium heat. When melted, add rice and stir to coat. Cook rice, stirring for about a minute.
Add white wine and cook, stirring, until evaporated.
Add tomato sauce, 1/2 cup at a time, stirring and cooking until mostly cooked down before adding more. Test rice after about 20 minutes for done-ness; it should be slightly chewy in the center.
If more sauce is needed, add water to the tomato sauce and quickly bring to a simmer before adding to the rice.
When rice is nearly done, taste, add salt and pepper as needed, then stir in cheese. Cover and let stand, off the heat, for about 5 minutes.
Stir in basil and serve with additional cheese and small basil leaves for garnish.