To prepare the sauce: In a medium saucepan, melt 1 tablespoon of the butter. Add the shallots and cook over moderate heat until softened, 4 minutes. Add the cream, wine and stock and bring to a boil. Simmer over moderate heat until reduced to 1 1/2 cups, 20 minutes. Remove from the heat and whisk in the remaining 5 tablespoons of butter, 1 tablespoon at a time. Add the sage, lemon juice and cayenne. Season with salt and white pepper and cover.
Meanwhile prepare the chicken: In a shallow bowl, combine the bread crumbs, panko, cheese, lemon zest and thyme. In another shallow bowl, beat the eggs. Season the eggs and chicken cutlets with salt and black pepper. Dip each cutlet in the egg mixture and let the excess drip off, then dredge in the bread crumbs. Transfer the breaded cutlets to a baking sheet lined with parchment paper.
Preheat the oven to 325°. In each of 2 large skillets, heat 1/4 inch of oil until shimmering. Working in batches, add the breaded cutlets and cook over moderately high heat for 1 minute. Lower the heat to moderate and fry, turning once, until the cutlets are browned and crisp, about 4 minutes. Transfer to paper towels to drain, then keep warm in the oven on another baking sheet while you fry the rest.
Rewarm the sauce over moderate heat, stirring constantly. Arrange the cutlets on plates, sprinkle with the parsley and serve with the sauce.