Season chicken thighs all over with salt and pepper. Heat olive oil in a 12-inch skillet over medium-high heat until shimmering. Add chicken skin-side down and cook without moving until deeply golden and crisp, 6-7 minutes. Flip and cook 2 minutes more, then transfer to a plate. The chicken will not be fully cooked yet.

Pour off all but 1 tablespoon of fat from the pan. Reduce heat to medium and add onion. Cook, stirring occasionally, until softened and just starting to color, 4-5 minutes. Add garlic, smoked paprika, and saffron; stir until fragrant, about 30 seconds. Add rice and stir to coat in the oil and spices, toasting lightly for 1-2 minutes.

Pour in warm broth and stir once to distribute. Nestle chicken thighs skin-side up into the rice, leaving some skin exposed. Bring to a gentle boil, then immediately reduce heat to low. Cover and simmer until rice is tender and chicken registers 165F at the thickest part, 18-20 minutes. Resist the urge to lift the lid early.

Scatter peas over the top, cover again, and remove from heat. Let stand 5 minutes so the peas warm through and the rice absorbs any remaining liquid. The bottom should have formed a light socarrat (crispy crust). Serve directly from the pan with lemon wedges for squeezing over.