Make the breadcrumbs: Cut crust from baguettes. Cut bread into 1-inch cubes; pulse in a food processor in batches to form coarse crumbs (this should yield 5 to 6 cups). Spread on a rimmed baking sheet; dry at room temperature for at least an hour or as long as overnight.
Prepare the chicken: Preheat oven to 200 degrees. Working with one at a time, place chicken breasts on a cutting board, flat side down. Press down on chicken with the palm of one hand, and cut in half horizontally to make 2 cutlets.
With the flat side of a meat pounder, pound chicken between pieces of plastic wrap until about 1/4 inch thick.
Lightly beat 3 large eggs in a medium bowl. Place 2/3 cup all-purpose flour and breadcrumbs in 2 separate wide, shallow dishes. Season eggs, flour, and chicken with coarse salt and freshly ground black pepper. Working with 1 cutlet at a time, dip into flour, turning to coat and shaking off excess. Dip into egg, and lift out, letting excess drip off. Dip into breadcrumbs, pressing firmly to help them adhere. Transfer to a plate or pan, and refrigerate at least 30 minutes and up to 2 hours. If needed, separate layers with wax paper or parchment paper.
Heat oil in a 12-inch skillet (oil should be between 1/4 and 1/2 inch deep) over medium-high heat until shimmering; a breadcrumb should sizzle instantly when dropped into oil. Gently place 2 cutlets 3/4 to 1 inch apart in skillet, and fry until undersides are golden brown, 3 1/2 to 4 minutes. Flip cutlets, and fry until cooked through and golden brown on other side, about 2 1/2 minutes more (chicken should feel firm).
Cutlets less than 1/4 inch thick will take 1 to 2 minutes less. Transfer to a paper-towel-lined baking sheet, and pat off excess oil. Lightly sprinkle with coarse salt, and keep warm in oven. Repeat with remaining cutlets, skimming brown bits and adding more oil if necessary. Aside from a squeeze of fresh lemon, a simple salad is all you need with chicken Milanese.