This is one of those annoying posts because I don't have a recipe to go along with the picture. That being said, I can point you to similar recipes and discussion of technique so you can experiment on your own. All good croissants are the same: a slightly sweet and leavened dough layered with fat. I used Peter Reinhart's recipe in Artisan Breads Everyday (another book of his I recommend) which adds the additional element of an overnight fermentation of the dough in the fridge for added flavour. I like this method because it means you work with a cold dough that helps keep the fat above room temperature.
So, let me impart some words of wisdom should you decide to embark on the adventure of croissant making. I completely messed up two batches of dough before I finally had success. Yes, there were a few tantrums and half-laminated dough may or may not have been thrown across the kitchen. Obviously, the main obstacle that needs to be overcome for the vegan croissant maker is replacing the butter. My experience is that Earth Balance Vegan Buttery Flavor Sticks work best. The key here is that you need a firm margarine that will not get too soft. I first used the whipped Earth Balance and that was a complete disaster. If the margarine is too soft it will squirt out from between the layers of dough. If your margarine gets too soft, put it in the fridge to firm up.
The second obstacle for any croissant baker is actually rolling out the dough. Here my advice is to be patient. You need to give the gluten time to relax so the dough can be rolled out. Be firm but gentle, if you know what I mean. Reinhart says to roll from the centre to the four corners first, then along the length and width. This is an excellent method that results in an almost perfect rectangle of equal width and depth. Keep your work surface well floured and be patient.
Most recipes I have seen call for an egg wash on the final dough. Reinhart thinks this is unecessary and I agree. As you can see from the pic above I had some problems getting the perfect crescent shape, but they tasted great. I also did not roll them tight enough, but no one seemed to care.
So, where to go for recipes? Vegan Lunch Box has a recipe with half whole wheat flour if you are so inclined. The recipe is also pretty simple and clear (Reinhart's recipe goes on for 8 pages, complete with pics. It is thorough for the first timer). This recipe is more detailed. Both of these recipes use pure butter, while Reinhart blends 2 tbsp with 1.5 cups of butter for the butter layer. Finally, here is the recipe from Foodbeam, the blog I used to make a vegan puff pastry.