The night before, set aside 1/2 cup of the cheese; wrap and refrigerate. Place one slice of ham on a clean work surface. Sprinkle with 1/4 cup of the remaining shredded cheese and top with a chicken breast half. Carefully roll up to enclose chicken. Place in the removable crockery liner of a 3 1/2- or 4-quart slow cooker. Repeat with remaining ham, cheese, and chicken breasts. Pour pasta sauce over chicken. Cover and refrigerate overnight.
The next day, let crockery liner stand at room temperature for 15 minutes. Place liner in the slow cooker unit. Cover and cook on low for 3 1/2 to 4 hours. Sprinkle with reserved 1/2 cup shredded cheese, toasted panko, and basil before serving. If desired, serve with hot cooked pasta.
From the Test Kitchen
To toast panko, heat a medium skillet over medium-high heat. Add panko and cook 2 to 3 minutes or until toasted, shaking skillet occasionally.