Combine chicken strips, 1/2 cup white wine, 1/2 cup chicken broth, and 1/2 cup lemon juice in a large resealable bag. Seal and place in the refrigerator for 1 hour to marinate.
Mix flour, oregano, basil, pepper, and salt in a bowl. Remove chicken strips from the marinade and dredge in the flour mixture. Discard marinade.
Pour Parmesan cheese onto a plate. Roll chicken strips in Parmesan cheese.
Melt 2 tablespoons butter in a skillet over medium-high heat. Cook chicken strips in batches until browned, 1 to 2 minutes per side. Transfer to a slow cooker.
Pour remaining 3/4 cup white wine, 3/4 cup chicken broth, 1/4 cup lemon juice, bouillon cubes, and garlic over chicken in the slow cooker. Cover and cook on Low until chicken is no longer pink in the center, 4 to 6 hours.
Transfer chicken to a plate using a slotted spoon. Drizzle 2 teaspoons melted butter on top. Cover to keep warm.
Pour liquid from the slow cooker into a pot; add parsley. Bring to a boil. Reduce heat to low and stir in heavy cream and cornstarch. Simmer until sauce thickens, about 5 minutes. Pour sauce over chicken.