Using a mallet or rolling pin pound chicken breasts to even 1/2-inch thickness. Dissolve salt and sugar in 1 quart cold water in gallon-sized zipper-lock plastic bag. Add cutlets and seal bag, pressing out as much air as possible; refrigerate for 30 minutes.

Line a baking sheet with 3 layers of paper towels, place cutlets in single layer and cover with another 3 layers of towels. Press firmly to absorb as much moisture as possible. Allow cutlets to dry for 10 minutes. Meanwhile process bread pieces in food processor until evenly fine-textured, 20 to 30 seconds. You should have 1¼ cups fresh bread crumbs when done. Transfer crumbs to pie plate. Carefully peel paper towels off cutlets, sprinkle cutlets with pepper and set aside.

Adjust oven rack to lower-middle position, set heatproof plate on rack and heat oven to 200˚F. Spread flour in second pie plate. Beat eggs with 1 tablespoon oil in third pie plate.

Working one at a time, dredge cutlets thoroughly in flour, shaking off excess. Using tongs, dip both sides of cutlets in egg mixture, coat thoroughly, allowing excess to drip back into pie plate to ensure very thin coating. Dip both sides into bread crumbs press with fingers to form even cohesive coat. Place breaded cutlets in singe layer on wire rack set over baking sheet and allow coating to dry about 5 minutes.

Meanwhile, heat 6 tablespoons oil in heavy-bottom 10-inch nonstick skillet over medium-high heat until shimmering but not smoking, about 2 minutes. Lay 2 cutlets in skillet; cook until deep golden brown and crisp on first side, gently pressing down on cutlets with metal spatula to ensure even browning, about 2 to 3 minutes. Using tongs, flip cutlets, reduce heat to medium and continue to cook until meat feels firm when pressed gently and second side is deep golden brown and crisp 3 minutes longer. Line plate in oven with paper towels and set cutlets on top and return plate to warm oven.

Discard oil in skillet and wipe clean. Repeat with another 6 tablespoons of oil and cook remaining cutlets as before.

Serve with lemon wedges.