Prep the chicken: Pat the chicken breasts dry with paper towels. If they’re very thick, lightly pound to an even 3/4-inch thickness so they cook evenly.
Season both sides with salt and pepper. Go easy on the salt—prosciutto is salty.
Make the herb mixture: In a small bowl, combine garlic, thyme, rosemary, smoked paprika, lemon zest, and 1 tablespoon of olive oil. Stir to form a paste.
Coat the chicken: Rub the herb mixture over the chicken on both sides, pressing it in so it adheres.
Wrap with prosciutto: Lay two slices of prosciutto slightly overlapping on a board.
Place a chicken breast on top and wrap the prosciutto around it, tucking the ends underneath to secure. Repeat with remaining chicken.
Sear for crispiness: Heat a large oven-safe skillet over medium-high heat. Add the remaining 1 tablespoon oil and the butter.
When hot and foamy, place the chicken seam-side down. Sear 2–3 minutes per side until the prosciutto is lightly browned.
Finish in the oven: Transfer the skillet to a 400°F (200°C) oven. Roast 10–14 minutes, depending on thickness, until the internal temperature reaches 165°F (74°C).
If you don’t have an oven-safe skillet, move the chicken to a preheated baking sheet after searing.
Rest and serve: Let the chicken rest 5 minutes. Spoon any pan juices over the top and serve with lemon wedges. A quick squeeze of lemon brightens the salty-savory flavors.