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In a large heavy saucepan, heat the olive oil and the butter over medium-high heat. Add the onions and cook, stirring, for 2 minutes. Add the garlic and cook until fragrant, about 30 seconds. Add the rice and cook, stirring constantly, until opaque, 2 minutes. Add the wine and cook, stirring until the rice nearly completely absorbs all the liquid, about 1 minute.
Reduce the heat to medium, add 1 cup of the hot stock, and cook, stirring constantly. Cook the risotto, adding more stock 1/2 cup at a time as it is absorbed, about 20 minutes total cooking time. Stir in the green onions after 15 minutes cooking time. Season the risotto with 1 teaspoon of salt and 1/2 teaspoon of white pepper. The rice should be slightly al dente.