'Nduja is a spicy, spreadable salami that adds tons of flavor to this dish.
Using a sharp knife, butterfly each chicken breast by cutting horizontally almost all the way through. Open each piece like a book; pound between sheets of plastic wrap until about 1/8 inch thick. Season the chicken with salt, pepper, and the rosemary.
Heat a large nonstick griddle or cast-iron skillet over medium-high. Add 2 tbsp. olive oil, two turns of the pan. Add the garlic. Stir until fragrant, about a minute. Remove the garlic. Working with 2 pieces at a time, cook the chicken until browned, about 3 minutes. Turn and spread about 1 oz. ’nduja on each. Top with half the cheese. Cover the pan with foil and cook until the cheese melts and the chicken is cooked through, about 1 minute. Transfer to plates. Add the remaining 2 tbsp. oil to the skillet and repeat with the remaining chicken, ’nduja, and cheese. Top with the cherry peppers.
In a large bowl, toss the kale, lemon juice, and EVOO.
In a large nonstick skillet, melt the butter over medium heat. Crack in the eggs. Cook for about 3 minutes for set whites and runny yolks. Top each pizzette with an egg. Serve with the salad.