Melt 2 tbls. butter with oil in a 12" heavy skillet. Add the chicken; cook until the juices run clear when pricked with a fork, about 3-5 minutes on each side(don't overcook!). Remove chicken, set aside.
Melt 2 tbls. butter in the same skillet. Add mushrooms and cook over medium high heat until tender, about 5-8 minutes. Set asie.
Arrange the cooked broccoli in a single layer in the bottom of the buttered baking dish.
Season the chicken with some lemon pepper seasoning(to taste), and arrange in single layer over broccoli.
Melt remaining 2 tbls. butter in a 1 quart saucepan. Whisk in flour; cook over low heat, stirring constantly, about 3 minutes. Pour in chicken stock and wine, whisking until completely blended. Continue cooking and stirring until the sauce thickens enough to coat a spoon. Add 1 1/2 cups Swiss cheese, stirring until melted. Taste and season with salt and pepper.
Pour sauce over chicken; arrange mushrooms on top. Sprinkle additional cheese over dish to garnish.
Broil about 6" from heat source until the top is bubbly and golden.