In a medium-sized bowl, mix together diced beets, sweet potato, parsnip, and carrot. Toss the root vegetables with olive oil and salt.
Spread vegetables on a roasting pan or Pyrex baking dish in a single layer.
Bake for 15 minutes.
Remove from the oven, toss, and spread vegetables again in a single layer.
Bake for another 15 minutes or until the vegetables are fully cooked.
Reduce oven heat to 375 F.
Line two cookie sheets with Silpats or parchment paper.
Cut each sheet of puff pastry into four squares.
Place four puff pastry squares onto each cookie sheet.
Place 1/4 cup of roasted root vegetables in the center of each square.
Drizzle approximately 1 teaspoon of maple syrup and sprinkle ¼ teaspoon cinnamon on top of each pile of vegetables.
Starting with one of the squares, fold one corner of the puff pastry dough to the corner diagonally across from it, overlapping the edge by 1/8 inch and forming a triangle. Run your thumb along the entire folded edge and press down to tightly seal the opening. Repeat on each square until you have sealed all eight turnovers.
In a small bowl, beat the egg.
Brush egg on top of each turnover.
Sprinkle 1/4 teaspoon brown sugar on top of each turnover.
Bake for 20 minutes or until puff pastry is flaky and slightly brown.
Although there are specific root vegetables suggested in the recipe, any root vegetable combination will work as long as you have approximately 1 1/4 pounds raw, diced root vegetables.