In a 2-quart saucepan set over a medium high heat, add the olive oil and 2 tablespoons of the butter. Once the oil is hot and the butter is melted, add the orzo and toast lightly, about 3 minutes. Add the onions and cook, stirring, until soft, 3 to 4 minutes. Add the garlic and cook for 30 seconds, stirring. Add the wine, stir, and cook to deglaze the pan.

Once the wine has nearly evaporated, add 2 cups of the stock, stirring constantly until the stock has evaporated, about 5 minutes. Add the remaining 2 cups of stock, the salt, and white pepper, and cook until it has been absorbed by the orzo and the orzo is tender. Add the basil and stir to blend. Remove the pan from the heat and add the cheese. Stir in the remaining 2 tablespoons of butter and the tomatoes and adjust the seasoning, to taste.