Put butter, garlic, fresh thyme, salt, pepper and wine in the saucepan add mushrooms and cook about 10 - 12 minutes. Mix cornstarch with 1/2 cup cold water, add to the mushrooms and cook additional 2 minutes. Let cool complicity, I usually cook mushrooms day before.
Take 2 phyllo sheets and brush with oil, cover remaining phyllo sheets with a damp kitchen towel to prevent drying.
Add 1/2 cup cold mushrooms, roll into the shape of big spring roll. Put on the baking sheet covered with parchment paper and brush with oil.