1. Thaw the mushrooms in a bowl if frozen, reserving the liquid that collects in the bottom of the bowl. Separate the caps and stems and drain the caps well on paper towels. Squeeze the liquid from the stems into the, bowl. Finely chop the stems and add to the liquid. Place the stems and liquid, cream, and tarragon in a small saucepan. Heat the liquid to a boil over low heat and boil until there is just enough liquid to coat the mushroom stems, about 2 minutes. Season the liquid to taste with salt and pepper. Set aside.

2. Preheat the oven to 400°F. Using some of the melted butter, grease a mini muffin tin with cups about 1½ inches across the top by ½ inch deep.

3. Arrange the phyllo sheet with one of the long edges facing you. Brush the right half, of the phyllo with melted butter. Fold the left side over the buttered side to make a double-thickness. Brush and fold again to make a 4-layer pile of phyllo about 4½ inches wide × 14 inches long. Cut the rectangle crosswise into 3 equal pieces (each piece will be about a 4½-inch square). Cut each square into 4 even squares. You should have 12 squares altogether. Line the cups of the muffin tins with the phyllo squares. There should be enough dough to completely line the cups, with the points extending over the rim of the cups.

4. Place a mushroom cap, gill side up, in each of the phyllo-lined cups. Spoon the cream mixture over each cap, coating the cap completely. Sprinkle the grated cheese, if using, over the cream mixture.

5. Bake until the phyllo is deep golden brown and crisp and the filling is bubbling and lightly browned, about 10 minutes. Remove and cool for 2 minutes before removing the cups from the muffin tins to serve.