Heat the griddle and paella pan to medium-high. Drizzle with olive oil and add the onion, garlic, and bell peppers. Sauté until softened, about 5 minutes.
Add the rice to the pan and stir to coat with oil. Toast for a minute or two until slightly translucent.
Stir in the smoked paprika and cook for 30 seconds.
Gradually add the hot broth, one ladleful at a time. Let the rice absorb the liquid before adding the next ladleful. This should take about 20-25 minutes, until the rice is almost cooked through.
While the rice cooks, cook the chicken and chorizo on the griddle in batches on a separate part of the griddle. Sear until golden brown on both sides.
Once the rice is almost cooked, add the chicken, chorizo, and peas to the paella pan. Stir gently to combine.
Increase the heat to high and cook for a minute or two to form a slight crust (socarrat) on the bottom of the paella.
Turn off the heat, cover the pan, and let the paella rest for 5-10 minutes.
Serve the paella garnished with chopped parsley and lemon wedges.