Pollo Grigliato Ripieno

Name: Pollo Grigliato Ripieno
Ingredients: ¼ cup Extra Virgin Olive Oil, divided; 2 tbsp White Cooking Wine; 2 cloves Garlic, minced; 8 oz. Sliced Baby Bella Mushrooms (White mushrooms are fine, too.); 4 Boneless Skinless Chicken Breasts, butterflied; ¼ cup Sun Dried Tomatoes, divided into 4 parts; 2 oz. Goat Cheese, divided into 4 parts; 12 oz. Capellini (Or other thin long pasta); ½ Lemon, zested; 2 tbsp Capers; 1 cup Grated Parmesan Cheese (Fresh grated off a cheese block is ideal); ¼ oz. Fresh Basil, torn or chopped, divided