Preheat grill. Toss shrimp with kosher salt and fresh black pepper, 2 tablespoons olive oil, and 2 teaspoons garlic in medium bowl, set aside. Season chicken thighs with salt, set aside.
Heat 2 teaspoons olive oil in paella pan until shimmering but not smoking. Add peppers and cook, stirring occasionally, until skin begins to blister, about 3 minutes. Transfer peppers to plate and set aside.
Add 1 tablespoon oil to paella pan, heat until shimmering but not smoking. Add chicken thighs in a single layer, cook without moving for 3-4 minutes, flip and cook additional 3 minutes on second side. Chicken does not need to be cooked through but should be brown. Transfer chicken to bowl. Reduce heat to medium and add chorizo, cook, stirring frequently, until deeply brown and fat has rendered, about 4-5 minutes. Transfer chorizo to bowl with chicken and set aside.
Add enough oil to rendered fat in paella pan to equal 2 tablespoons total. Heat over medium heat until shimmering but not smoking. Add onion and cook, stirring frequently, until softened. Stir in remaining garlic and cook until fragrant, about 1 minute. Add sofrito and stir until mixture begins to darken and thicken slightly, about 3 minutes. Add rice, stir until well coated with sofrito mixture. Stir in chicken broth, white wine, saffron, bay leaves, paprika, and 1/2 teaspoon salt. Return chicken and chorizo to pan, increase heat to medium high and bring to boil, uncovered, stirring occasionally. Close grill lid and cook until rice absorbs most of the liquid, about 15 minutes. Test rice, if it is not tender add a little more chicken stock and cook a little longer.
When rice is just about done (tender, most of the liquid is absorbed) scatter shrimp over rice, insert mussels hinged side down into rice, arrange bell pepper in a pinwheel pattern over the paella and scatter peas over the top. Cover again, cooking until shrimp is opaque and mussels have opened up.
Increase heat to high, cook for an additional 2-3 minutes without stirring to develop soccarat crust.
Remove from grill, sprinkle with parsley and serve with lemon wedges.