Cook the broccoli according to your package's directions (I usually just microwave it in a bowl with a few tablespoons of water until it's done). Drain and transfer to a 9" x 13" baking dish and set aside.
Heat oil and 2 tablespoons butter in a 10" skillet over medium-high heat. Add mushrooms, and cook, stirring, until browned, about 5 minutes; transfer to a bowl and set aside.
Add 3 tablespoons butter to skillet and melt. Remove from heat add bread crumbs and sage; season with salt and pepper and set aside.
Heat remaining butter in a 2-qt. saucepan over medium-high heat. Add garlic and onion, and cook until soft, about 4 minutes. Add flour, and cook, stirring, for 2 minutes. Add milk, mustard, and nutmeg, and bring to a boil. Reduce heat to medium and cook, stirring often, until sauce is slightly thickened, about 3 minutes. Remove from heat and stir in cream cheese, 1 cup cheddar, mayonnaise, and eggs until smooth; season with salt and pepper and set sauce aside.
Heat broiler to high. Pour sauce evenly over the top of the broccoli; sprinkle with mushrooms, bread crumbs and remaining cheddar. Broil until cheese is melted and lightly browned, about 2 minutes.