In an oven-safe medium sauté pan over medium-low heat, sauté onion in olive oil. Cook 10 to 12 minutes, stirring occasionally, or until onion begins to caramelize around the edges. Add cherry tomatoes. Cook an additional 5 to 7 minutes, stirring occasionally, or until vegetables have caramelized. Add garlic, and cook 1 to 2 minutes until fragrant.
In a medium bowl, whisk eggs with milk, thyme and a hefty pinch each salt and pepper. Add egg mixture to sauté pan, turning pan to ensure liquid is in an even layer. Top with asparagus spears. Cover and cook until frittata is puffy and eggs are almost set, about 10 minutes.
Heat oven to high broil.
Sprinkle Grand Cru cheese over frittata. The middle of the frittata may still be liquid, but it will finish cooking under the broiler. Place under the broiler and cook until cheese is bubbling and golden.
To serve, garnish with additional thyme, and cut into quarters.