Preheat oven to 350 degrees F. Position rack in center.
Remove all the meat from the lobster and roughly chop, leaving some large pieces. Set aside
Melt 2 tablespoons of butter in a small skillet, saute scallions for 2 to 3 minutes. Add lobster meat and wine, stir quickly to combine over high heat. Drain the mixture, reserving the liquid. Set lobster meat and scallion mixture aside. Melt remaining butter in another skillet. Add flour and cook slowly without coloring or about 5 minutes. Add reserved liquid and cream. Cook, stirring constantly until mixture begins to thicken. Stir lobster meat back into the mixture, add cayenne, and season to taste. Cool mixture completely.
Rinse chicken breasts and pat dry. Trim any fat around edges. Place breasts, 1 at a time, between sheets of waxed paper and gently pound with a mallet until about 3/8-inch thick. Season with salt and pepper to taste.
Lightly oil a 13 by 9-inch baking pan. Place 1/4 cup stuffing on the center of the underside of each breast. Bring the top and bottom flaps of the chicken up over the stuffing, slightly overlapping the ends, then fold up the sides to enclose the stuffing completely. Lay the packets seam side down in the pan and brush with olive oil.
Bake until chicken is lightly browned and feels firm when pressed, 20 to 30 minutes. Slice each roll on the diagonal to serve.