Preheat oven to 375F/191C. Line a baking sheet with parchment paper. Add olive oil to a medium skillet. Sauté the onion over medium heat until the onions are translucent.
Once translucent, add coconut sugar and increase to medium-high heat to caramelize. Cook until brown and slightly crispy. Remove from pan and set aside.
Heat olive oil in a small saucepan. Sauté sliced mushrooms and minced garlic in the olive oil.
Set mushrooms on a plate lined with several paper towels. Fold paper towels completely around mushrooms, turn over and let them sit to absorb excess moisture.
Carefully unfold puffed pastry onto parchment paper (you may also use a lightly floured surface). You may use a rolling pin to spread the dough out a little if you want. Spread the caramelized onions over the over the center of the puff pastry leaving about a ¾ inch border at the edge of each side of the pastry.
Next, top with mashed sweet potato.
Follow with mushrooms in an even layer.
Drizzle Dijon mustard over top of all ingredients. Sprinkle with sea salt and black pepper, then top with fresh rosemary.
Carefully roll the pastry over the top of the mushroom mixture until you have a lovely log. Press down to seal the edges.
Gently roll the log over so the seam is on the bottom.
In a small bowl, whisk together ingredients for vegan egg wash. Using a pastry brush, brush the top of the pastry with a light coat. Using a sharp knife, cut lines across the pastry one way, and then the other in a cross-hatch pattern. Place in freezer for 10 minutes. Remove and reapply a thin coat of vegan egg wash.
Bake in a preheated oven at 375F/191C degrees for about 40 minutes, depending upon your oven. It's done when the crust turns a nice, golden brown. Remove from oven and allow to cool for 10 minutes before slicing. Enjoy!