Add stock, paprika and saffron to a pot and heat, covered.
In a separate 15" paella pan, add 2 tbsp olive oil and brown the chicken pieces and chorizo, about 5 minutes. Remove. Add the remaining olive oil and cook the onions over medium heat until translucent, about 5 minutes. Add the bell peppers and cook for a few minutes. Add the tomatoes and garlic and simmer for another 5 minutes, until they have a sauce-like appearance. Salt and pepper to taste.
Pour in the rice and stir until the rice is covered with the tomato mixture (known as 'sofrito'). Add chicken and chorizo pieces. Slowly add all of the broth to the paella. Stir the rice mixture around until it is evenly distributed throughout the pan. Important - do not stir after this point.
Simmer for about 10 minutes, then place the shrimp and shellfish into the mixture one-by-one, evenly distributing throughout. Simmer for another 15 minutes, or until all of the broth has been absorbed, adding extra liquid if necessary.
Remove from heat, gently cover with foil and let sit for another 10 minutes. Garnish with piquillo pepper slices and lemon wedges.