For the fries: Line a baking sheet with fries and bake 25 minutes to very crispy.
Stem and gill (scrape underside of caps with teaspoon) the mushrooms and wipe with damp towel to remove grit. Thinly slice the mushrooms. Melt 3 tablespoons of butter in large skillet over medium-high heat and when it foams add the mushrooms. Brown well until meaty in fragrance and well browned.
Halve, peel and thinly slice onions and peel garlic. In a second large skillet over medium heat, melt 2 tablespoons butter then add the onions and season with salt, white pepper and bay leaf. Cook until tender, 8 to 10 minutes, stirring occasionally. Turn the heat up to medium-high to high, add about 3/4 cup water and let it absorb completely. Then lower heat to low and remove bay leaf.
While onions cook, grate or chop the garlic. Add to mushrooms along with thyme, salt, black pepper, sherry, Marsala or wine, Worcestershire and soy sauce. Reduce heat to low.
For the cheese sauce: In a sauce pot, melt butter over medium-high heat. Whisk in flour, add milk and while it thickens grate provolone. Add it and the cheddar in small handfuls to sauce.
Top the fries with mushrooms, sweet, soft onions, cheese sauce, chopped giardiniera and/or cherry pepper rings and serve. OR layer slices of provolone on a roll with mushrooms, onions and chopped giardiniera.