Preheat oven to 350°F/175°C/Gas mark 4. Brush any dirt away from the mushrooms (do not submerge in water), and chop into medium size chunks (smaller than bite sized, but not minced).
Melt butter in large skillet over medium heat and add shallot and garlic to the pan. Stir frequently until softened, about 1 or 2 minutes. Careful not to burn or it will taste bitter.
Add chanterelles and season with salt and pepper. Cook and continue to stir frequently until mushrooms have softened and released some of their liquid, about 5 minutes.
Raise heat to medium-high and add the dry vermouth and parsley. Continue to cook until liquid has mostly evaporated, but not totally dried out, about 3 minutes more. Taste and season with more salt and pepper if needed.
Make sure your phyllo is thawed, but keep it covered so it doesn’t dry out.
Butter or grease your tart pan (I like the kind with the removable bottom just so I can see the sides later).
Place one layer over half of the pan, then another layer of the other half of the pan, overlapping a little. Lightly brush phyllo layer with melted butter. Rotate pan about 15 degrees and repeat with additional layers of filo and butter.
Layer the Gruyere cheese on top of the layers of phyllo dough (reserving a small amount – a few tablespoons for the topping).
Spread the mushroom mixture on top of the cheese, then evenly distribute the Parmesan cheese along with the remaining Gruyere cheese.
Gently bring the phyllo dough up and over the mushrooms and slightly crumple it, then lightly brush with melted butter.
Bake for 30-35 minutes or until the phyllo is golden brown. You may need to rotate half way through if your oven does not heat evenly.