Preheat oven to 425 degrees.
Melt the oil and butter in a large skillet over medium heat.
Add the fennel and onion to the skillet and stir well.
Add the salt and pepper to the skillet and cook the fennel and onion, stirring occasionally, for approximately 4-5 minutes.
Add the broth to the pan, scraping up any browned bits from the bottom of the pan. Continue cooking over medium heat for an additional 2-3 minutes.
Turn off the heat and stir the mayonnaise, mozzarella and Romano cheese to the fennel mixture and stir well to combine.
Spray a small 1½ quart casserole dish or gratin dish with olive oil or cooking spray.
Spoon the fennel and onion mixture evenly into the dish.
Bake the fennel-onion gratin in a preheated oven for 30-35 minutes, or until the gratin is golden and bubbly.
Cool slightly before serving.