Bring chicken broth to a boil in a big skillet with a lid. Add chicken and return to boil. Reduce to medium low heat. Cover and poach chicken (8 mins.)
In a skillet saute shallots in oil and butter for 2 mins. Sprinkle in flour and cook 1 min. Whisk wine and reduce by half, about a min. Ladle in chicken broth whisking sauce as you do. Stir in heavy cream. Season with nutmeg, salt, and pepper. Bring to a bubble and reduce heat to low. Slice chicken into 1/2 inch slices and put in pan with sauce.
Preheat Broiler
Simmer broccoli spears in 1" of water, covered for 5 mins. Drain and put in a shallow baking dish. Layer half the grated cheese and chicken recipe. Top with remaining cheese brown until bubbling and golden under broiler, about 2 mins. Serve.