1. Preheat oven to 400°F (200°C).
2. Heat a sauté pan over medium-high heat and add half of the butter.
3. Add broccoli and radishes to the pan along with turmeric, salt, and pepper. Sauté until just starting to brown, about 5-7 minutes.
4. Add mushrooms and remaining butter to the pan. Sauté until mushrooms release their juices, about 5-10 minutes more.
5. Reduce heat to low, add tomatoes and basil, and stir to incorporate.
6. In a separate bowl, whisk together eggs, milk, salt, pepper, and cayenne. Stir in half of the shredded cheese.
7. Transfer vegetable mixture to a glass baking dish.
8. Pour egg mixture over vegetables and top with remaining cheese.
9. Bake for 30 minutes at 400°F.
10. Allow to cool slightly before slicing and serving.