Preheat oven to 350 and lightly grease a small casserole baking dish.
In a medium skillet, over medium heat, saute spinach, diced mushrooms and grated garlic. Season with some salt and pepper and cook until mushrooms are done. Place the mixture in a bowl and mix with 3/4 cup of Asiago cheese. Set aside to cool until it can be handled.
Slice chicken breasts in two, width-wise (like you would butterfly it but all the way through). Place a chicken breast in a thick zip-lock bag and pound it carefully, do not pound too hard and be careful not to make any holes. Repeat with remaining chicken breasts. (You may have to use more than one bag if you make too many holes in one.) Salt and pepper pounded chicken and set aside.
Mix Panko bread crumbs with 1/4 cup of Asiago cheese, some salt and pepper and set aside.
Divide spinach mixture over the chicken breasts.
Roll up each chicken breast, tightly. Bread rolled chicken by pressing it in bread crumb mixture on all sides.