Use a sharp knife to carefully butterfly each chicken breast, creating a pocket without cutting all the way through. This allows space for the stuffing.
Season the inside and outside of each chicken breast generously with salt, pepper, and smoked paprika, ensuring even coverage for flavor.
Heat a skillet over medium-high heat, then add olive oil. Once shimmering, place the chicken breasts in the pan and sear for about 3-4 minutes, until they develop a golden-brown crust.
Remove the chicken from the pan and carefully open each pocket. Divide the sun-dried tomatoes, mozzarella slices, and chopped basil evenly among the pockets.
Fold the chicken breasts over the filling, pressing gently to seal the edges.
Return the stuffed chicken to the skillet. Cover with a lid and cook on medium heat for 8-10 minutes, until the chicken is cooked through and juices run clear. Use a meat thermometer to ensure an internal temperature of 165°F (74°C).
Once cooked, remove the chicken breasts from the skillet and let them rest for 5 minutes to allow juices to redistribute.
Slice the chicken breasts crosswise to reveal the gooey cheese and colorful filling inside. Serve immediately for a juicy, cheesy, and smoky flavor explosion.