Pat the chicken thighs dry and season generously with kosher salt and freshly ground black pepper. Heat the olive oil in a paella pan or large, wide skillet over medium-high heat. Add the chicken, skin side down, and cook until golden brown on all sides, about 6–8 minutes. Transfer the chicken to a plate and set aside.
Reduce the heat to medium. Add the chopped onion and bell peppers to the pan and cook, stirring occasionally, until softened and translucent, about 10–15 minutes. Add the minced garlic and cook until fragrant, about 1 minute.
Stir in the crushed tomatoes and cook, stirring, until the sauce thickens and darkens slightly, about 5–7 minutes. Sprinkle in the paprika and add the bay leaf, stirring quickly so the paprika doesn’t burn. If using, steep the saffron threads in a small amount of warm broth and stir them in now.
Add the rice and stir constantly for about 2 minutes to coat the grains in the tomato mixture. Nestle the chicken pieces back into the pan. Pour in the hot chicken broth.
Increase the heat to bring the liquid to a gentle boil. Then reduce the heat to medium-low and simmer, uncovered and without stirring, until the rice is tender and most of the liquid is absorbed, about 15–18 minutes.
About halfway through cooking (around 8–10 minutes), sprinkle the peas evenly over the rice.
Remove the pan from the heat when the rice has almost absorbed all the liquid. Cover the pan with a clean kitchen towel or aluminum foil and let it rest for 5–10 minutes.
Serve directly from the pan with lemon wedges on the side, if desired.