In a small saucepan, bring the stock to a simmer. Remove from the heat and cover to keep warm.
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.
Remove from the heat. Add the cheese, nasturtiums, and chervil, and stir well to mix. Adjust the seasoning, to taste, with salt and pepper. Garnish with chives and serve immediately.