Preheat oven to 300 F
Cut parsnip in half lengthwise. If it is a large parsnip, cut it into 4 pieces.
Cut carrot lengthwise in half.
Place carrots, parsnips and onions on a well oiled baking sheet and place in oven. After 10 minutes add shitake mushrooms.
Bake for 10-15 more minutes or until everything is soft.
Remove from oven and let cool to room temperature.
Place all ingredients in a food processor and puree for 3 minutes.
Remove ingredients from processor, place in a medium sized bowl and refrigerate for 30 minutes.
Form mixture into 2 6 ounce patties or 4 3 ounce patties.
Place medium fry pan on medium heat with 2 ounces of oil in it.
Flour each side of the patty and fry till golden brown on each side.
Place patty in a 350 F oven for 5 minutes and serve.