Preheat oven to 375° and line a small baking sheet with parchment paper. In a medium bowl, whisk together oil, soy sauce, maple syrup, paprika, and liquid smoke. Place baby carrots in a Ziploc bag, then cover with the marinade. Marinate 30 minutes in the refrigerator.
Drain carrots and pat them dry with paper towels. Place carrots on prepared baking sheet and bake for 15 minutes. Remove from oven and let cool.
Cut puff pastry dough into squares and roll a carrot into each square.
Cover the baking tray with a parchment paper and put the each wrapped carrot on it.