Preheat oven to 400° F and line a baking sheet with parchment paper; set aside.
Thinly slice white and light green part of the leek, then rinse well. Melt butter over medium heat and sauté the leek until tender, about 10 minutes. Remove heat and set to the side.
While leeks cook, prepare puff pastry. Unfold pastry on a floured surface, roll into a 10-inch x 15-inch rectangle, and then transfer to the prepared baking sheet (I like to gently fold it into a square to transfer it, then unfold it once it’s on the baking sheet).
Use a sharp knife to score a border around the pastry dough 1-inch from the edges on all sides, making a rectangle, but DON'T cut all the way through the pastry (see picture). Then prick the pastry all over with a fork inside of the rectangle (do not prick outside the scoreline). Lightly brush pastry with olive oil and sprinkle with everything bagel seasoning.
Bake pastry for 10 minutes. When it comes out of the oven the center may be puffy. Make prick holes again with a fork and gently press the center down so that it's flat and the outside edges are puffy.
While the pasty cooks, whisk together eggs and milk in a medium bowl. Mix in gruyere, fontina, parmesan, parsley and sautéed leeks. Evenly spread mixture over baked puff pastry, leaving the 1-inch border. Lay asparagus crosswise over cheese mixture (see pictures). Lightly drizzle with olive oil, season with salt and pepper, and sprinkle with a small handful of parmesan cheese.
Bake for 20-25 minutes until set and asparagus is tender but slightly crunchy.
Meanwhile, fry bacon over medium heat until crispy, about 7-10 minutes. Once cool enough, crumble bacon.
Once the tart is done baking, remove from oven, sprinkle with crumbled bacon, and let cool for a couple minutes. If desired, sprinkle with additional shaved parmesan and fresh parsley.
Slice and serve warm!