Combine half of the butter and all the oil in a heavy 4-quart (3.8L) pot over medium-high heat. Add the onion and cook, stirring with a wooden spoon, until the onion begins to soften, 2 to 3 minutes. Be careful not to brown it. Stir in the rice to coat the grains with the fat and onion mixture, and cook about 1 minute longer.
Add the wine and cook, stirring, until it is mostly absorbed by the rice. Begin to add the broth, 1/2 cup (118ml) at a time, stirring well after each addition. Wait until each addition is almost completely absorbed before adding the next 1/2 cup (118ml). Reserve 1/4 cup (59ml) of the broth to add at the end.
When the rice is tender but firm, in about 20 minutes, turn off the heat. Add the remaining 1/4 cup (59ml) broth and the other half of the butter, the cheese, salt and pepper to taste, and stir well to combine with the rice. Serve immediately.