Heat a large nonstick skillet over medium heat; melt butter in the oil; then add fennel and onion; cook 15-20 minutes, stirring frequently, until onion and fennel carmaelize or turn golden brown and are sweet to taste.
While the fennel and onion cook, beat eggs with a whisk for 3 minutes; season with salt and pepper.
Pour eggs over fennel and onion; cook until eggs are firmly set, lifting up set egg from bottom occasionally to allow liquids to settle.
When frittata is firm, place on center rack in oven and broil until top begins to brown.
Cover top with fontina slices and place back under broiler until cheese just melts.