Add the flour, sugar, yeast and salt to a large bowl and whisk to combine.
Slice the cold vegan butter into slices (about 1/8 inch thick) and toss in the flour mixture with a spatula. Don't use a mixer; this will break up the butter too much. You want to simply toss it into the flour mixture.
Pour in the milk and and stir until a stiff, rugged dough with chunks of butter forms. Do not use your hands too much, you don't want to melt the butter at all.
Wrap the dough tightly in plastic wrap (or other eco-friendly wrap) and chill in the refrigerator for 1 hour.
After an hour, take the dough out of the refrigerator and place on a lightly floured surface. Roll the dough into a long rectangle-type shape. It will be messy and not look smooth at first, but it will get smoother as you fold and roll the dough.
Fold the dough into thirds like you would fold a letter (see photos above for reference). Roll it out into a large rectangle, then turn the dough 90 degrees, and repeat the rolling/folding process 5 more times. You should see large streaks of butter but the dough should be smooth. If the butter starts to soften in the middle of this, return to the refrigerator or freezer until stiff again.
Wrap tightly in plastic wrap again and chill in the refrigerator for another hour.
Divide the dough in half (this makes it easier to work with) and roll one half into a large rectangle (about 20 inches long, 10 inches wide and 1/8 inch thick). With a pizza cutter, trim away an uneven edges to make a clean rectangle.
Slice the dough into smaller rectangles, then into triangles (see photos in post above). Cut a small slit at the wide end of the triangle, then tightly roll up into a crescent shape, making sure the tip is tucked underneath.
Place on a parchment lined pan and cover loosely. Allow the croissant dough to rise for 1 hour at room temperature, then place in the freezer or refrigerator for 30 minutes.
While the croissants are chilling, preheat the oven to 375 degrees F.
In a small bowl, stir the maple syrup and soy milk together.
Gently brush the syrup/milk mixture onto the dough, then place in the center rack of the oven and bake for 20-25 minutes, or until puffy and golden brown. Remove from the oven and enjoy.