Trim the stem ends from the mushrooms. Place ⅓ of the mushrooms in the largest bowl of a food processor fitted with the S-blade. Pulse until finely chopped and transfer the chopped mushrooms to a bowl; repeat with remaining mushrooms in 2 more batches. The mushrooms should have some texture to them—don't process them down to a paste! (Alternately, you can use a chef's knife to chop the mushrooms.)
Melt the butter in a large skillet over medium heat. Add the shallot and garlic and cook until softened, 3-5 minutes. Stir in the mushrooms and a pinch or two of salt. Continue to cook, stirring often, until the mushrooms have released their liquid, about 7 minutes.
Increase heat to medium-high to cook off the remaining liquid; once the liquid has evaporated, after about 3 minutes, add the sherry to the skillet. Stir and continue to cook until the sherry evaporates and the skillet is dry. Remove from heat and stir in the parsley and salt and pepper to taste.
To make the sandwiches:
Heat a large griddle over medium heat. Butter one side of four slices of bread; place the buttered side of the bread onto the griddle. Divide half of the cheese onto the slices of bread, then spoon the duxelles over the cheese, top the duxelles with the remaining cheese and slices of bread. Butter the tops of the sandwiches.
Once the bottom of the sandwich is golden brown carefully flip the sandwiches over and cook until that side is also golden brown (about 5 minutes on each side). Transfer to plates and serve.