Prepare a grill for medium heat. Put a rimmed sheet pan on the grill to preheat. Pour the broth into a small saucepan and bring to a simmer over low heat. Add the saffron and keep hot.
When the grill is preheated, add the olive oil to the sheet pan. Add the chorizo and cook, tossing occasionally, until browned on the edges, 2 to 3 minutes. Add the onion and bell pepper and sprinkle with some salt. Cook, stirring occasionally, until the vegetables begin to wilt, about 3 minutes. Add the garlic and cook, 30 seconds. Add the rice and stir to coat the rice in the oil. Spread the rice with the back of a wooden spoon to make a flat even layer. Add the broth and adjust the heat so the edges are just simmering. Cover with a second inverted sheet pan, making sure the edges line up to create a tight seal. Weight the sheet pan down with the saucepan or a cast-iron skillet. Close the grill and let the rice simmer for 18 minutes. (If your grill has a thermometer, try to keep it between 350 and 375 degrees F.)
Check the rice. It should be cooked but still rather al dente. If not, give it a stir and cook a few more minutes. Uncover the grill and increase the heat to medium-high. Scatter the mussels and shrimp over the rice. Cover the grill and cook until the mussels just begin to open, 5 to 7 minutes. (This requires some attention: the rice should crust at the edges but not burn. Stir so that you can look at the rice to make sure, and adjust the heat accordingly.) Scatter the peas and scallions over the top. Cover and grill, checking occasionally, until the mussels and shrimp are cooked through, 8 to 12 minutes more. Drizzle the paella with olive oil and garnish with the parsley.
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