Preheat oven to 375 degrees. Heat stock in a medium saucepan over medium-low heat; season with salt and pepper.
Meanwhile, heat 3 tablespoons oil in a large saucepan over medium heat. Add onions and a pinch of salt; cook, covered, until translucent, 6 to 8 minutes. Add garlic; cook, stirring, until fragrant, about 1 minute. Stir in carrots, celery, and remaining tablespoon oil; season with salt and pepper; cook for 2 minutes. Stir in cumin and oregano. Add white wine; increase heat to medium-high. Cook until almost all of liquid is evaporated, 3 to 4 minutes. Stir in tomatoes; reduce heat to medium. Season with salt and pepper; cook for 2 minutes. Stir in turkey and rice.
Add heated stock to pot; bring to a boil. Season with salt and pepper. Stir in peas; simmer until rice is just covered with liquid. Cover, and transfer to oven. Bake for 20 to 25 minutes. Let stand, covered, for 5 minutes. Fluff rice with a fork. Stir in parsley. Serve immediately.