Thaw your puff pastry overnight in the fridge or on the counter for about 30 minutes.
Preheat the oven to 425 degrees. Cover a baking sheet with foil and lightly grease or spray with cooking spray. Set aside.
To prepare the filling, begin by dicing the onion. Heat a large nonstick skillet 0ver medium heat, add butter and the onion and cook for about 5 minutes, stirring occasionally. Add the garlic, meatless crumbles, and water to the onions. Cook for another 8 minutes.
Place the onion mixture in a medium bowl. Add 1 egg, panko bread crumbs, soy sauce, ketchup, mustard, and Vegemite. Mix well. Allow to cool.
While the filling is cooling, prepare the puff pastry. Flour a countertop, place one puff pastry sheet on the floured surface. The sheets start as 10"x 15", with a floured rolling pin, roll to about 15" x 18". Cut the sheet into thirds (a pizza cutter is helpful for this) that measure about 5" x "18 each.
Place about 1/6 of the filling in the middle of one of the rectangles. Gently bring both edges of the sheet together to form a roll and press edges together. Roll over so the seam is facing downward. Cut the roll into about 6 pieces. Gently place on the baking sheet with foil leaving an inch or two between each piece so they can rise.
Repeat the steps for the rest of the pieces. You'll likely have to bake in 2 or 3 batches in the oven, so don't try to fit them all on one tray.
To make your egg wash, place your remaining egg in a small bowl and beat with a fork. Set aside.
When your baking sheet is full, gently brush each roll with the egg wash and bake for 18-20 minutes until golden brown. Serve with ketchup.