Preheat the Oven: Preheat your oven to 180°C (350°F). Lightly grease a 9x13-inch (or similar size) baking dish and set it aside.
Prepare the Broccoli: In a pot, bring salted water to a rolling boil. Add the broccoli florets and blanch them for 3 to 4 minutes until they turn vibrant green and are slightly tender. Drain the broccoli and quickly plunge it into a bowl of ice water to halt the cooking. Once cooled, drain again and set aside.
Sauté the Vegetables: In a spacious skillet, warm the olive oil over medium heat. Add the diced onion and sauté for 3 to 4 minutes until it becomes soft and translucent. Incorporate the grated carrot, diced bell peppers, and a dash of salt. Continue cooking for an additional 5 minutes, until the vegetables are just tender. Mix in the chopped parsley and take off the heat.
Prepare the Casserole Base: In a large mixing bowl, whisk together the eggs, milk, and heavy cream. Add the flour gradually, whisking until smooth and free of lumps. Stir in the Greek yogurt, mayonnaise, minced garlic, and curry powder. Season with salt and black pepper to taste.
Assemble the Casserole: Spread the blanched broccoli florets evenly across the bottom of the prepared baking dish. Layer the sautéed vegetables and halved cherry tomatoes on top of the broccoli. Pour the egg and cream mixture over the vegetables, making sure everything is evenly covered.
Add the Cheese: Sprinkle the grated cheese evenly over the top of the casserole.
Bake the Casserole: Place the casserole in the preheated oven and bake for 30-35 minutes, or until the top is golden brown and the casserole is set in the center.
Garnish and Serve: Remove the casserole from the oven and let it cool for a few minutes before serving. Garnish with chopped fresh dill and additional parsley if desired.