Wash the mushrooms and carefully remove the stems. To remove the stems use your hands and hold the mushroom in the palm of one hand, and with your other hand turn the stem 180 degrees one way, then 180 degrees the opposite way. The stem should pop right out.
Chop stems and set aside.
Arrange the mushroom caps in a large baking dish or in 2 deep dish pie plates that will fit all the caps.
Melt the butter in skillet over medium heat. Add the olive oil and minced garlic and saute for about 2 minutes.
Add the chopped mushrooms and ground chicken to the skillet and saute until the chicken is cooked through.
Salt and pepper to taste.
Add the white wine to the pan and cook, stirring for 5 minutes.
Remove from heat.
Use a teaspoon to fill each of the mushroom caps with the chicken mixture.
If there is extra chicken mixture spread it around the caps and pour the pan juices over.
Top the mushroom caps with the grated cheese.
Sprinkle with the minced basil.
Bake 30-45 minutes until the mushrooms have released their liquid and the cheese is lightly browned.
Serve in the baking pan with your favourite bread to mop up the garlicky wine juices.