Bring a large pot of water to a boil, salt it, add the orzo and cook until al dente. Drain and transfer to a bowl.
While the pasta is working, preheat the oven to 400°. Spread the green beans on a rimmed baking sheet and drizzle with 2 tablespoons EVOO; season with salt and pepper. Roast until browned and tender, 12 to 15 minutes.
In a large, deep skillet, heat 1 tablespoon EVOO, 1 turn of the pan, over medium-high heat. Add the chorizo and cook for 1 minute. Add the onion, bell pepper, jalapeno and garlic, season with salt and pepper and cook for 5 minutes. Season the shrimp with the paprika and add to the mixture. Add the tomatoes and cook until the shrimp are pink and firm, 5 minutes. Stir in the remaining 1 tablespoon EVOO, the cheese and parsley.
Serve the spicy shrimp with the orzo and green beans.