Preheat oven to 400 F (205 C). Thaw puff pastry sheet on lined round (preferably) baking sheet for 30-40 minutes, just until it's pliable enough to roll. Once ready, roll out on a hard floured surface into a large round circle. Transfer back to lined baking sheet.
While puff pastry is thawing, caramelize your shallots by melting vegan butter into a small skillet. Add shallots and sauté until browned, about 5-7 minutes. Sprinkle with brown sugar, stir and sauté another 5-10 minutes until shallots are dark, sticky and sweet.
To a medium bowl, add sliced sweet potatoes, olive oil, sea salt and black pepper. Toss gently until thoroughly coated.
Arrange sweet potatoes and caramelized shallots onto bottom of puff pastry. Leave about 2 inches on all sides for fold over.
Fold edges over and smooth. Top with vegan feta cheese.
Brush crust with olive oil. Bake for 45-50 minutes until puff pastry dough is golden brown. Allow to completely cool before topping with pepita gremolata. Slice and serve.