Combine the flour, half of the garlic, 1 teaspoon salt and a few grinds of pepper in a large bowl; set aside. Combine the milk, paprika, oregano, the remaining garlic, 1 teaspoon salt and a few grinds of pepper in another large bowl. Add the chicken, turning to coat; set aside 15 minutes.
Toss the fennel and fronds, romaine, parsley, 2 tablespoons olive oil, the lemon juice, and salt and pepper to taste in a bowl.
Heat the remaining 3/4 cup plus 2 tablespoons olive oil and the peanut oil in a large cast-iron skillet over high heat until a deep-fry thermometer registers 350 degrees F. Dredge the chicken in the flour mixture; add to the skillet skin-side down. Fry 8 minutes. Flip; reduce the heat to medium high. Fry until golden and cooked through, 8 more minutes. Transfer to a rack. Blot with paper towels; season with salt. Serve with the salad.