In a medium saucepan, caramelize the carrots, celery, and onion in 2 teaspoons of the olive oil. Add the celery root, cover three-quarters of the way with water, and cover the pan. Slowly braise for 45 to 60 minutes, or until tender. Remove the celery root from the braising liquid and cool completely. Reserve the braising liquid. Trim the celery root to square off- and slice paper thin. Clean the Portobello mushrooms by removing the stems and the dark brown underside. Cut into quarters, season with salt and pepper, and drizzle with 2 teaspoons of the olive oil. Place in an ovenproof pan with the garlic and rosemary and cover with aluminum foil. Bake at 350 degrees for 30 to 40 minutes, or until tender.
In a medium saute pan, saute the diced celery and shallot in 1 teaspoon of the olive oil. Dice the roasted mushrooms and toss with the celery mixture and herbs. In a saute pan, wilt the Italian parsley in 1 teaspoon of the olive oil and 1 tablespoon of the braising liquid. Place the celery root slices on a sheet pan with a dash of the braising liquid, season with salt and pepper, and bake at 350 degrees for 3 to 4 minutes to reheat.
Lay 1 slice of the celery root on a plate and top with the mushroom and celery mixture. Place a piece of the parsley on top and cover with another piece of the celery root. Press the edges of the celery root together and place small pinches of braised Italian parsley at each corner. Drizzle with Red Wine Reduction around the edges of each plate.