Preheat the oven to 350°F.

Season the chicken on both sides with salt and pepper. Set out three shallow plates in assembly-line fashion. Put the flour in one, the beaten eggs in the next, and the bread crumbs in the third. Dredge each seasoned chicken breast in the flour, shaking off the excess, then dip in the eggs, and finally press them into the bread crumbs to coat thoroughly on both sides. Set the breaded chicken on a plate.

Heat a large ovenproof sauté pan over medium-high heat, and add the oil. Brown the chicken breasts on both sides until golden, about 3 minutes per side; regulate the heat as necessary to achieve a uniformly browned crust.

Transfer the pan to the oven and cook the chicken until cooked through, 10 to 15 minutes. Transfer the chicken to a rack to rest briefly.

Meanwhile, combine the wine, vinegar, shallot, chile, and bay leaf in a saucepan, bring to a boil over medium-high heat, and cook until the pan is almost dry. Add the cream and simmer until it reduces to about a teaspoon. Whisk in the butter little by little over medium-low heat until the sauce is creamy and emulsified. Strain the sauce through a fine-mesh strainer into a bowl. Add salt and pepper to taste and the juice of the lemon half.

Slice the chicken on the bias and arrange on serving plates. Spoon the sauce over the cop and garnish with the diced tomatoes and capers.