Use a sharp knife and cutting board to slice each chicken breast horizontally into thin cutlets, about 1/2 inch thick. This helps them cook quickly and evenly, perfect for searing.
Pat the sliced chicken dry with paper towels to remove excess moisture, ensuring a good sear and preventing steaming.
Combine salt, black pepper, and smoked paprika in a small bowl, then generously season both sides of each chicken cutlet, pressing the spices in lightly.
Heat olive oil in a cast iron skillet over medium-high heat until shimmering and just starting to smoke, about 2 minutes.
Carefully place the seasoned chicken slices into the hot skillet, laying them flat without crowding the pan. You should hear a sizzle.
Cook the chicken for about 3-4 minutes without moving it, until the edges turn golden brown and the underside develops a caramelized crust.
Flip each piece using tongs and cook for another 3-4 minutes, checking for a deep golden crust and firm texture.
Check doneness with an instant-read thermometer; the internal temperature should reach 74°C (165°F). The juices should run clear when pierced.
Remove the chicken from the skillet and let it rest on a plate for 5 minutes, allowing the juices to redistribute and keeping the meat tender.
Squeeze fresh lemon over the rested chicken to brighten the flavors, and serve immediately with your favorite sides.