In a large bowl, whisk the eggs, almond milk, sea salt, and a generous amount of black pepper together until well combined.
Warm the olive oil in a skillet over medium heat. Sauté the shallots with a pinch of salt until they’re soft and translucent. Add the broccoli and water, cooking until the broccoli is vibrant and tender.
Arrange the sautéed vegetables in the greased pie dish, creating an even layer. Evenly sprinkle the Gruyere cheese over the veggies. Gently pour the egg mixture over the cheese and vegetables. Shake the dish slightly to ensure the mixture settles evenly. Garnish with thyme or chives.
Bake in the preheated oven for 30 to 40 minutes, or until the quiche is set and the top is lightly golden. Let it cool slightly before slicing.