Preheat an oven. Remove the leaves, then roughly chop and set aside. Cut the stems into small long pieces.
Heat unsalted butter and extra virgin olive oil in a skillet over medium-high heat. Add water spinach stems, sliced leeks, and sliced shallot. Season with kosher salt, then cook, then add the water spinach leaves. Stir occasionally and cook.
In a large bowl, whisk together heavy cream, large eggs, grated fontina, grated Parmesan, remaining kosher salt, black pepper and chopped thyme leaves. To this, stir in the sautéed veggies and uncooked water spinach leaves.
Spray a pie dish or 10-inch quiche pan with nonstick cooking spray, then pour the quiche batter on top.
Place the quiche on a parchment or aluminum foil-lined rimmed baking sheet. Bake until the top is a light golden brown and the center of the quiche is mostly firm. Allow to cool. Can be enjoyed warm, room temperature, or cold.