Preheat a grill pan over medium high to high heat.
Scrape the gills off the underside of portobello mushroom caps with a spoon. Brush caps gently with a damp cloth to clean them. Drizzle caps with oil to keep them from sticking to the grill pan and season the caps with steak seasoning or salt and black pepper.
Grill mushrooms 3 or 4 minutes on each side under a loose tin foil tent until just tender. Remove from heat and cool 5 minutes.
Slice grilled caps into 1/2-inch strips. Turn strips in egg, then coat in mixture of parsley, bread crumbs and cheese. Cook "fries" over medium high heat in enough extra-virgin olive oil to coat a nonstick skillet in a thin layer, about 1/4 cup. "Fries" will brown in 2 or 3 minutes on each side.
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