Preheat your oven to 180°C (350°F).
Wash and cut fresh broccoli into bite-sized florets, or measure out frozen broccoli. Boil a large pot of salted water and blanch the broccoli for about 3-4 minutes.
In a mixing bowl, combine your choice of cheeses, eggs, yogurt or sour cream, salt, and thyme. Whisk until creamy and smooth.
Drain the blanched broccoli and add it to the cheese mixture. Stir gently to coat the broccoli evenly.
Drizzle olive oil in the baking dish to coat the bottom.
Pour the broccoli and cheese mixture into the prepared baking dish and spread evenly. Bake for about 25-30 minutes until the top is golden and bubbly.
Let cool for a few minutes before serving.