Heat 1 tablespoon of olive oil in a large Dutch oven over medium heat until shimmering. Add shrimp shells and cook, stirring often, until browned (2 to 4 minutes). Remove from heat, stir in wine, and scrape up browned bits. Cover and let steep.
Heat remaining 2 tablespoons of olive oil in the Dutch oven over medium-high heat. Add onion and bell pepper, cooking until softened and browned (5 to 7 minutes). Stir in garlic, paprika, saffron, red pepper flakes, and bay leaves, cooking until fragrant (30 seconds). Add tomatoes (with juice) and brandy, scraping any browned bits. Cook until slightly thickened (5 to 7 minutes).
Strain the shrimp shell mixture into the Dutch oven, pressing to extract liquid. Discard solids. Simmer the broth gently.
Add clams to the pot, cover, and cook for 4 minutes. Add mussels and scallops, cover, and cook until the shellfish begin to open (about 3 minutes). Add shrimp on top, cover, and cook until shrimp are opaque and scallops are firm (2 minutes).
Discard any unopened clams or mussels. Stir in picada and parsley, and season with salt and pepper to taste. Serve immediately in shallow bowls with lemon wedges and crusty bread.