In a large bowl, whisk together the flour, remaining 2 tablespoons of sugar, and salt. Cut the cold vegan butter into the flour (with a pastry cutter or knife) until there are only pea-sized chunks remaining.

Stir in the yeast mixture and egg. Mix until just combined. Wrap the dough in plastic wrap (it will be a bit sticky and soft before refrigerating; this is normal). Refrigerate for 30 minutes.

Unwrap the dough and place on a well-floured surface. Roll the dough out into a circle, ½-inch thick. Fold the dough in half to form a semicircle, then fold in half again. Roll the dough out again into a rough circle ½-inch thick. For a second time, fold the dough into a semicircle and then in half again.

Wrap the dough in plastic and refrigerate for 30 minutes.

Line a baking sheet with a silicone baking mat or parchment paper. Unwrap the dough and place on a floured surface. Roll the dough into a large rectangle to about 1/8-inch to 1/4-inch thick . Slice the rectangle horizontally into four even sections, then cut each of those sections into about 6 or 7 triangles. You should end up with a total of about 24 to 28 thin triangles (each about 6 inches long).

Roll each triangle from the widest end to the thinnest point. Place the rolls on the baking sheet. Cover loosely with a clean kitchen towel (or warm damp paper towel) and set aside at room temperature for 45 minutes.

Meanwhile, preheat the oven to 400 degrees.

Bake the rolls at 400 degrees for 10 to 14 minutes, or until golden brown. Cool slightly and serve warm.