Heat oven to 350◦F. Generously grease 11x17-inch baking dish with butter; set aside.
Bring large pot of salted water to boil; add pasta and cook to al dente, according to package directions. Remove pasta from heat and drain well; set aside.
In small saucepan over medium-high heat, combine milk and cream and bring to low simmer. In large saucepan over medium-low heat, melt butter. Once butter is completely melted, whisk in flour, cayenne pepper and nutmeg. Cook 30 seconds, add garlic and cook 1 minute.
Whisking constantly, gradually add warmed cream mixture to butter mixture and cook until sauce starts to thicken, about 3 minutes. Reduce heat to low. Slowly add parmesan, asiago and 3 cups of fontina. Continue stirring until cheeses are completely melted. Add peas and asparagus and cook for an additional 2 minutes. Remove from heat.
Fold cooked pasta into sauce, stirring until noodles are well coated. Pour mixture into prepared baking dish, sprinkle with remaining fontina and bake uncovered 45 minutes, or until the top is golden brown and sauce is bubbling. Top with fresh parsley and serve warm.