Preheat the oven to 450°. Lightly oil a large, rimmed baking sheet. Heat the olive oil in a medium saucepan. Add the shallot and garlic and cook over moderate heat until softened, about 4 minutes.
Add the rice and cook, stirring, for 30 seconds. Stir in the water and bring to a boil.
Cover and simmer over moderately low heat, stirring occasionally, until the water has been completely absorbed, about 10 minutes.
Scrape the rice into a bowl and let cool to room temperature.
Stir the Gruyère, 1/4 cup of the Parmesan and all of the chopped herbs into the rice.
Season the rice with salt and generously season with coarsely cracked pepper.
In a medium stainless steel bowl, beat the egg whites with a pinch of salt until firm peaks form.
Stir one-fourth of the whites into the rice to loosen the mixture, then stir in the remaining whites. Roll the rice into 1 1/2-inch balls.
In a shallow bowl, toss the panko with the remaining 1/4 cup of Parmesan. Dredge the rice balls in the panko crumbs and transfer to the prepared baking sheet.
Bake the rice balls in the upper third of the oven for 25 minutes, or until golden and crisp. Let stand for 5 minutes, then transfer to a platter and serve.