Heat 1 tablespoon olive oil in a medium pan. Add the onions and cook on medium heat, stirring constantly for 5 minutes until caramelized. Add balsamic and continue to cook until evaporated. Remove from heat and set aside.
Cut parsnips into strips
Preheat oven to 450 degrees. Toss parsnips with 1 tablespoon olive oil and spread out on a large rimmed baking sheet. Roast for 10 minutes; turn parsnips and roast until parsnips are tender and browned in spots, 10–15 minutes longer. Meanwhile in a clean pan heat a tablespoon of oil. Sear the veggie patties for about 3 minutes per side.
Toast the buns. Layer veggie burgers on buns, top with caramelized onion, your favorite burger toppings and a lettuce leaf. Serve burgers with Parsnip fries.