Heat olive oil in a skillet over medium heat and sauté the broccoli until bright green and slightly tender with lightly browned edges.

Add the halved cherry tomatoes to the skillet and cook briefly until they soften and release a fragrant, slightly sweet aroma.

Stir in the rinsed white beans and chopped thyme, warming everything together for a minute so the flavors begin to blend.

In a large mixing bowl, whisk the eggs with the half-and-half until smooth and slightly frothy.

Add salt, black pepper, shredded Gruyère, and grated Parmesan to the egg mixture, stirring until evenly combined.

Spread the vegetable and bean mixture evenly across the prepared baking dish.

Pour the egg and cheese mixture over the vegetables, ensuring the filling is evenly distributed.

Gently shake the dish to help the custard settle around the vegetables.

Bake until the center is set and the top turns lightly golden with a delicate cheesy crust.

Allow the quiche to cool for several minutes before slicing so the texture becomes firm and easy to serve.