1. Preheat the oven to 180°C (350°F).
2. Peel and finely chop the garlic and shallot together. Set aside.
Slice the mushrooms and set aside.
3. Pour olive oil into a frying pan and heat over high heat.
Add the garlic-shallot mixture, sliced mushrooms, and cook for 5 minutes.
4. Bring a large pot of water to a boil, then add the asparagus spears and broccoli florets and cook for 5 minutes.
Drain the asparagus and set aside.
5. (optional) Grease the gratin dish with butter.
6. In a bowl, mix together the breadcrumbs, grated Parmesan cheese, and heavy cream.
Pour half of the breadcrumb-cream mixture into the bottom of the dish.
7. Add the mushrooms in an even layer.
Cover the mushrooms with the remaining cream mixture.
Arrange the cooked asparagus on top.
8. (optional) Sprinkle with grated cheese.
9. Bake for 15 to 20 minutes.
10. Sprinkle with chopped basil before serving.