Bring a large saucepan of salted water to boil. Add potatoes and cook until tender. Drain, peel, and using a potato ricer, rice potatoes into a large bowl. Add butter, cheese, and salt and pepper to taste. Mix thoroughly.

Line 4 (8-ounce) ramekins with plastic wrap. Fill with potato mixture. Press down firmly to create a dense potato cake and smooth the tops.

Preheat oven to 350°F. Season chicken with salt on both sides; pat 3 tablespoons ground pepper onto the top-side of breasts.

Heat vegetable oil a large heavy skillet over medium-high heat. Add chicken and cook on both sides until nicely browned, about 6 minutes per side. Remove from heat. Transfer chicken to a baking pan, reserving skillet. Tightly wrap baking pan with aluminum foil, place in oven and bake chicken until cooked through, about 20 minutes.

Return skillet to medium heat; add butter and shallots. Sauté for 5 minutes, add mushrooms, and continue cooking until mushrooms have softened, 5 to 7 minutes more. Add brandy to deglaze the pan. Let brandy cook for 1 to 2 minutes, then whisk in cream and herbs. Reduce heat to medium-low and allow sauce to reduce until nicely thickened, 10 to 12 minutes. Remove from heat, and cover to keep warm.

While the sauce is reducing, remove potato cakes from ramekins, remove plastic wrap dust tops and bottoms of cakes with flour. Heat a large skillet with some vegetable oil over medium-high. Place cakes into skillet and cook until golden and well crusted, about 5 minutes per side.

Place one potato cake on each plate, lean one chicken breast against potato cakes and spoon brandy mushroom sauce over top. Serve with St. Francis 2003 Zinfandel, Pagani Vineyard Reserve, Sonoma Valley.