Preheat oven to 425 degrees Fahrenheit/220 degrees Celsius.
Melt vegan butter in a saucepan. Add the flour and saute for a couple of minutes, stirring constantly. You'll know when the roux is done when it smells aromatic and loosens up. It will be lightly blonde in color.
Stir in the milk slowly, mixing or whisking as you go, to keep lumps from forming. Once you have a smooth sauce, stir in nutmeg, pepper and red pepper flakes, if using. Mix. Cook the sauce a couple more minutes until it begins to thicken and coats the back of a spoon.
Stir in the vegan cheese, reserving some shreds for the top, and mix in. Add salt to taste. Turn off heat.
Roll out the puff pastry sheet on a lightly floured surface. It should be approximately 14 inches long and 9 inches wide. Transfer the puff pastry carefully to a baking sheet.
With a knife, carefully score a one-inch edge along the border of the puff pastry, taking care not to cut all the way to the bottom. Spread the bechamel sauce evenly inside the scored border.
Layer the trimmed asparagus spears over the bechamel sauce. Brush lightly with olive oil and sprinkle on some salt and pepper. You can also sprinkle on a few more cheese shreds over the asparagus at this time.
Bake for 20-25 minutes or until the puff pastry is golden brown and puff. Cool on a rack for five minutes, then slice and enjoy!