Preheat the oven to 375 degrees F. Heat the olive oil in an ovenproof pot over medium heat. Add the onion and thyme and cook until the onion is slightly softened, about 2 minutes. Stir in the rice and cook, stirring, until glossy, 1 to 2 minutes. Add the wine and cook, stirring, until it's absorbed, about 1 minute. Add 1 teaspoon salt, and pepper to taste.
Pour the broth and 1 1/2 cups water over the rice and bring to a simmer, about 4 minutes. Stir, then cover and transfer to the oven. Bake 20 minutes, stirring halfway through.
Meanwhile, cook the peas in 4 cups salted boiling water until tender, about 5 minutes. Reserve 1 cup cooking water, then drain.
Remove the rice from the oven. Stir in the peas, 1 tablespoon horseradish, the parmesan, and salt and pepper to taste. Stir in enough of the reserved cooking water until the rice is creamy. Divide among bowls. Top with the trout, the remaining tablespoon horseradish, and baby greens, if desired. Drizzle with olive oil.