Heat a large cast-iron skillet over medium-high. Loosen the skin on one chicken breast, creating a pocket. Arrange 1 sliced garlic clove and some chopped rosemary under the skin. Repeat with the remaining chicken breasts, 3 cloves garlic and rosemary. Season the chicken with salt and pepper.
Coat the bottom of the skillet with 2 tbsp. EVOO, two turns of the pan; add the chicken, skin side down. Weigh down the chicken with a skillet or a foil-covered brick; cook until the skin is crisp, about 12 minutes. Turn and cook until the chicken is no longer pink in the center, 5 to 6 minutes more. Transfer the chicken to a plate.
Add the wine to the skillet and stir, scraping up any browned bits. Simmer until the sauce is reduced to 2 to 3 tbsp.; drizzle over the chicken. Add the remaining EVOO and garlic; stir 30 seconds. Add the escarole and stir until wilted, about 3 minutes. Season with salt, pepper and nutmeg. Stir in the stock, then squeeze the lemon half over the greens.
Divide the chicken and escarole among plates. Mop up the pan juices with slices of the bread and serve on the side.