If the chicken breasts have tenderloins attached, remove them and reserve for another use. Place the breasts between 2 sheets of plastic wrap and gently pound them to a uniform thickness of 1/2-inch.
In a shallow dish (a pie plate works well), beat the egg together with the milk. Spread the breadcrumbs on a plate or sheet of wax paper and combine with 1 teaspoon of salt and a few grinds of black pepper. Dip each chicken breast in the egg, then coat with breadcrumbs.
Heat about 1/8-inch of olive oil in a large frying pan over medium-high heat. Add the chicken in a single layer and fry until golden-brown and cooked through, 3 minutes per side. Transfer to a platter and set aside.
Wipe the pan clean and add 1 tablespoon of oil. Reduce the heat to medium and add the shallots. Sauté the shallots until softened, 2 to 3 minutes, then whisk in the honey, thyme and cream.
Return the chicken to the pan and carefully turn each piece several times until the breadcrumb coating has absorbed the sauce. Serve immediately.