In a bowl, combine goat cheese, basil, oregano, thyme, lemon rind, salt and pepper; set aside. (Make-ahead: Refrigerate in airtight container for up to 8 hours.)
With sharp knife held horizontally and starting at thinner side, cut each chicken breast in half almost but not all the way through; open like book. Place between sheets of plastic wrap; pound with mallet to even thickness.
Roll 2 tablespoons of the filling into a log shape; place into crease of chicken breast. Fold top and bottom over ends of log; fold side edges of chicken over log to overlap. Turn chicken over so seam is underneath. Repeat with remaining chicken. (Make-ahead: Cover and refrigerate for up to 8 hours.)
Brush chicken with oil; sprinkle with salt and pepper. Place on greased rimmed baking sheet. Roast in 375 degree oven until chicken is cooked through about 20-30 minutes.
In a bowl, cover tomatoes with boiling water; let stand until softened, about 10 minutes. Drain and dice.
In large skillet, melt half of the butter over medium heat; fry onions until very soft and golden brown, about 20 minutes. Transfer to bowl.
Increase heat to medium-high. Add remaining butter; saute mushrooms and garlic until softened, about 5 minutes. Return onions to pan. Add sherry; cook until reduced by half, about 3 minutes. Stir in tomatoes.
Add stock and cream; bring to boil, reduce heat to medium-low and simmer until sauce is thick enough to coat back of spoon, about 4 minutes.
Slice each chicken breast on angle into 4 pieces. Spoon sauce onto plates; arrange chicken over sauce.