Preheat your oven to 400°F and lightly grease your pie dish.
Heat the oil in a large skillet over medium-high heat. Add the zucchini, garlic, pepper flakes, salt and pepper. Cook, stirring, until lightly tender but not overly soft, about 5 minutes. Remove from heat and let cool slightly.
Roll the puff pastry sheet out to larger than the size of your pie plate. Press the pastry into the dish, folding over and gently stretching until it fits your dish, trimming excess off the edges.
In a large bowl, whisk together the eggs, milk, and Dijon until well combined and frothy.
Add ¾ of the cooked zucchini in an even layer to the puff pastry crust. Then, add ½ of the crumbled goat cheese on top.
Pour the egg filling into the pastry. Top with the remaining zucchini slices and the goat cheese crumbles.
Transfer to the preheated oven and bake, uncovered, until the filling is set and the crust is golden brown, 30 to 40 minutes. If the top is starting to look overly browned, tent with a piece of foil. You want your eggs to be set; however, you want it to have a bit of a wobble to it as it comes out of the oven. It continues to cook and set as it rests and the wobble will ensure it has a silky, not rubbery, texture.
Remove from the oven and let cool for 5-10 minutes before slicing. Serve and enjoy!