In a small saucepan, bring the stock to a simmer. Remove from the heat and cover to keep warm.
In a large skillet, heat 2 tablespoons of the oil over medium-high heat. Add the peppers and cook, stirring frequently, until cooked through but still slightly crunchy, about 5 minutes. Remove from the heat and set aside.
In a large heavy saucepan, heat the remaining 2 tablespoons olive oil and the 2 tablespoons 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 and stir in the thyme. 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 and cooked bell peppers 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.
Remove from the heat. Discard the thyme sprigs. Add the cheese and prosciutto, and stir well to mix. Adjust the seasoning, to taste, with salt and pepper. Serve immediately.