Step 1: Prepare the chicken. Pound boneless, skinless chicken breasts to an even 1/2-inch thickness.
Step 2: Set up your dredging station. In one shallow dish, combine flour, salt, pepper, garlic powder, and paprika. In a second shallow dish, whisk eggs and milk. In a third shallow dish, place Panko breadcrumbs.
Step 3: Bread the chicken. Dredge each chicken breast first in the seasoned flour, shaking off excess. Then dip into the egg mixture, allowing excess to drip off. Finally, coat thoroughly in the Panko breadcrumbs, pressing gently to adhere.
Step 4: Heat oil. Pour vegetable or canola oil into a large heavy-bottomed skillet or Dutch oven to a depth of about 1-2 inches. Heat over medium-high heat until a thermometer reads 350-375°F (175-190°C).
Step 5: Fry the chicken. Carefully place 1-2 chicken breasts into the hot oil, ensuring not to overcrowd the pan. Fry for 4-6 minutes per side, or until golden brown, crispy, and the internal temperature reaches 165°F (74°C). Remove to a wire rack set over paper towels to drain. Repeat with remaining chicken.
Step 6: Prepare the buns and lettuce. Lightly toast the brioche or potato buns. Toss the chopped romaine lettuce with a tablespoon or two of Caesar dressing.
Step 7: Assemble the sandwiches. Spread Caesar dressing on both halves of each toasted bun. Layer with the dressed romaine lettuce, then a crispy fried chicken breast, and finally, a sprinkle of freshly grated Parmesan cheese. Top with the other bun half and serve immediately.