Pre-heat the oven to 425°F.
Arrange the potato wedges on a baking sheet and toss to coat lightly in EVOO. Season liberally with salt and pepper and roast for 40-45 minutes, until deeply golden and crisp, turning once. When the fries are done, melt the butter in a small pan over medium heat until it foams. Add the chopped garlic and swirl it around for a minute or two to infuse the butter. Toss the fries in large bowl with the garlic, butter, parsley and paprika.
Heat a large, cast iron skillet or other ovenproof pan on the stovetop over medium-high heat. Add the EVOO, two turns of the pan, and brown the chicken pieces on both sides; remove to a plate. Add the chorizo to the skillet and lightly brown for a minute or so on each side; remove to a plate. Add the onion, garlic and the sweet and hot peppers to the skillet and season with salt and pepper. Douse the pan with sherry to deglaze; sprinkle with thyme. Add the reserved chicken and chorizo back to the pan and transfer to the oven to continue cooking for 15 minutes, until the juices run clear. Douse the pan with lemon juice, garnish with parsley and serve with the fries alongside.