Preheat the oven to 475F
Place the cubes of squash and chopped sage on a cookie sheet, drizzle with 1 tablespoon of the olive oil and roast until light golden brown, 8 to 10 minutes. Set aside in a large salad bowl to cool.
Place the Jerusalem artichokes on the same cookie sheet and toss with 1 tablespoon of the olive oil. Roast in the oven for 6 to 7 minutes. Remove and set aside with the squash.
Place the parsnips and the mushrooms on the cookie sheet and toss with cumin and one more tablespoon of the olive oil. Roast for 6 to 7 minutes, then set aside with the other vegetables.
Bring 6 cups of water to a boil and set up an ice bath near the stove. Plunge the leeks into the boiling water and cook until tender, 2 to 3 minutes. Remove the leeks from the boiling water and submerge them in the ice bath until cool. Remove the leeks from the ice bath, pat dry with paper towels and set aside.
Add the leeks, celery root and mizuna to the salad bowl. Add the remaining olive oil, the sherry vinegar, salt and pepper and toss gently to coat well.
Divide the mixture evenly among four chilled dinner plates, mounding it like a haystack. Gently place the frico against the stack.
For the Frico:
Place 3 tablespoons grated Montasio cheese in a mound on a silpat. Place under the broiler until the cheese is melted and begins to brown. Carefully remove the cheese with a spatula and shape as desired.