In a small pot, combine broth, saffron, Pimentón, and a 1/4 piece of the onion over medium heat. Cover and simmer for about 15 minutes. Discard onion. Keep over low heat.
In a 13 1/2 wide paella pan, drizzle olive oil over medium-high heat. Once heated, add the chicken pieces and sprinkle with salt. Cook, stirring often, until golden and no longer pink in the center. Remove to a plate.
Add the chorizo slices and cook, stirring often, until lightly fried. Chop the rest of the onion and add to the chorizo. Stir in the scallions, garlic, and piquillo peppers. Cook, stirring often, until onion is softened and translucent. Stir in the shrimp and cook until just pink. Remove the shrimp to the plate with the chicken. Stir in the rice, coating it in the oil. Add the parsley and bay leaf.
Add the hot chicken broth, wine, and peas. Season with salt and mix just until everything is distributed. Once the stock is boiling, reduce heat to medium and cook, undisturbed, until most of the stock has absorbed, about 10 minutes.
Evenly bury the chicken and shrimp in the rice. Press the mussels, hinge side down, a little into the rice so they are standing. Place the 4 shell-on shrimp on top of the rice. Reduce heat to medium low, cover, and steam until the mussels have opened and shrimp are pink, about 10 minutes.
Remove pan from heat and cover with foil. Let sit for 10 minutes.
Serve warm with lemon wedges and parsley.