Preheat the broiler. Line a large baking sheet with foil and place peppers on it. Broil peppers, turning occasionally, until blackened all over. Transfer peppers to a large bowl and cover tightly with plastic wrap. Let steam until peppers are cool enough to handle, about 15 minutes.
Peel and discard blackened skin from peppers. Discard seeds and stem. Place pepper flesh in a blender and add 2 cups chicken broth. Blend until completely smooth.
While peppers roast and steam, in a soup pot or Dutch oven over medium heat, brown sausage, breaking up meat with a wooden spoon. Add onion and garlic and sauté until softened, 6-8 minutes. Add tomatoes, orzo, blended pepper mixture, and remaining chicken broth. Bring to a simmer, cover, and cook, stirring occasionally, until orzo is tender, about 10 minutes.
Stir in spinach and cook just until wilted, about 1 minute. Serve garnished with parsley.