Prepare the grill for direct cooking over medium heat (350° to 450°F) and preheat a grill-proof Dutch oven or deep 12-inch cast-iron pot for 10 minutes.
Cut the fronds from the fennel stalks and roughly chop them. Set aside to garnish the stew. Cut off the thick stalks above the bulb and discard, cut the bulb into quarters, remove the thick triangular-shaped core, and then cut the quarters into thin slices.
Add the chorizo to the Dutch oven and cook over direct medium heat, with the lid closed, until browned, about 5 minutes, stirring occasionally. Using a slotted spoon, transfer the chorizo to a plate lined with paper towels.
Wearing insulated barbecue mitts pour off all but 1 tablespoon fat from the Dutch oven, if necessary. Add the fennel, onion, and oil to the Dutch oven, and then cook over direct medium heat, with the lid closed, until the vegetables are almost tender, 13 to 15 minutes, stirring frequently. Add the garlic and cook until fragrant, about 30 seconds, stirring frequently. Add the tomatoes, wine, thyme, paprika, salt, and pepper. Bring to a boil and continue cooking until the mixture is slightly thickened, 6 to 8 minutes, stirring occasionally. Add the mussels and cook, with the lid closed, until the shells open, about 5 minutes. Discard any mussels that do not open. Stir in the sausage.
Ladle the stew into bowls. Garnish with the chopped fennel fronds. Serve with crusty bread for dipping.