This recipe has become a regular in our cooking repertoire. Using three coatings for the chicken is a classic technique. By dipping the chicken breasts first in flour, the egg has something to hold on to. The egg coating provides additional moisture and flavor and holds the bread crumbs, which offer a crusty texture. If you get organized at the outset by assembling two baking sheets, two plates for the flour and bread crumbs, and a bowl for the eggs, then you just have to coat and sauté the chicken.

Steps

1. Place a long piece of plastic wrap on a work surface. Set chicken breasts, about 3 inches apart, on plastic, then cover with another piece of plastic wrap. Using a flat (nonserrated) meat pounder or bottom of a small saucepan, pound chicken so it is uniformly thin, without tearing it.
2. Organize the 3 coatings. Place flour on a dinner plate. In a shallow, wide bowl, beat eggs together; set next to flour. Combine bread crumbs, salt, pepper, sugar, and tarragon on another plate and set next to eggs. Have ready 2 baking sheets. Lightly coat each chicken breast first with flour, shaking off excess. Then dip in egg and let excess drain off. Finally, coat lightly but completely with crumb mixture. Place on baking sheets until ready to sauté. (This may be done up to 6 hours in advance. Cover tightly with plastic wrap and refrigerate until ready to cook.)
3. Heat a heavy, 12-inch frying pan (preferably cast iron) over medium-high heat, add oil and butter, and tilt to coat pan. (If sautéing chicken in 2 batches, preheat oven to 200°F.) Add chicken to pan without crowding and sauté until bread coating looks crisp and golden, 2 to 3 minutes per side. Sauté a second batch, adding additional oil and butter if needed. Keep first batch warm while sautéing second. Serve hot, garnished with lime wedges.