Preheat the oven to 350 degrees. Brush the cut sides of the squash with oil; season with salt and pepper. Roast, cut side down, on a rimmed baking sheet until tender when pierced with a knife, 40 to 50 minutes.
Meanwhile, heat 1 tbsp. oil in a medium saucepan over medium. Add the chorizo; cook, stirring often, until browned in spots, about 3 minutes. Add the onion and garlic; cook, stirring often, until the onion is translucent, 3 to 5 minutes. Add the rice, paprika and cayenne; stir 1 minute. Add the stock; bring to a boil. Reduce the heat to medium-low; cook, stirring occasionally, until the rice is al dente, 15 to 18 minutes. Stir in the peppers, peas and 2 tbsp. parsley; season.
Preheat the broiler. Turn the squash cut side up. Fill with rice mixture, mounding in center. Broil until browned in spots, 8 to 10 minutes. Drizzle with oil; top with parsley.