Rinse the chicken; pat dry with paper towels. Place each chicken breast half between 2 pieces of heavy plastic wrap. Working from center to the edges, pound lightly with the flat side of a meat mallet to 1/4 to 1/8 inch thickness. Remove plastic wrap.
In a small mixing bowl stir together the Boursin cheese and flour until smooth. Stir in the carrot, walnuts, and 2 tablespoons of the snipped parsley. Place one-fourth of the cheese mixture on each pounded chicken breast half.
To roll up the chicken, fold in 2 opposite sides, then roll up. Press edges to seal. Repeat to make 4 bundles.
For coating, in a small mixing bowl stir together the remaining parsley, the fine dry bread crumbs, and Parmesan cheese. Brush the chicken bundles with the milk. Roll bundles in the crumb mixture to coat. Place chicken bundles, seam sides down, on a wire rack in an 8x8x2-inch baking pan. Sprinkle with any remaining crumb mixture.
Bake in a 350 degree F oven for 40 to 45 minutes or until the chicken juices run clear and coating mixture is golden brown. Makes 4 servings.