Preheat oven to 375°. Flour a work surface and a rolling pin. Set puff pastry on surface, sprinkle lightly with flour, and roll out into a rectangle about 8 in. by 12 in. and 1/8 in. thick. Arrange pastry so that it's horizontal and trim edges even.
Drizzle or spoon 1/4 cup honey evenly over entire pastry (don't spread) and sprinkle half of pastry with 1/4 cup almonds. Fold honeyed half over almonds, like closing a book. Sprinkle top of pastry with flour and roll back out into a rectangle about 2/3 the size of the one you began with. Drizzle or spoon another 1/4 cup honey over entire pastry, sprinkle half with another 1/4 cup very finely chopped almonds, and fold honeyed half over. Roll with the pin a few times to seal.
With a sharp knife, cut pastry lengthwise into 1/3-in.-wide strips. Twist each strip loosely a couple of times and put on an ungreased baking sheet (push ends onto sheet to keep straw from untwisting; you may need 2 sheets). Put straws in freezer for 20 minutes so they firm up, then dab tops of strips lightly with egg wash and sprinkle with sugar.
Bake straws until medium golden brown, 12 to 15 minutes. Let cool 1 minute, then loosen gently from sheet with spatula. Serve warm or cool.