Marinate the chicken breasts in 1/2 cup white wine and 1/2 can of chicken broth for about an hour.
After marinating, heat grill up to medium heat. Grill chicken until done.
While chicken is grilling, heat up the remaining wine and chicken broth in small saucepan on medium high heat till boiling. Mix the cornstarch into the the half-n-half then pour into the wine/broth, stirring constantly, till thickened. Remove from heat and add the chopped basil. Set aside.
When chicken is done on the grill, turn the heat off (or put where there's less heat) and add a slice of ham covered by a slice of Swiss cheese. Allow cheese to melt then remove to serving plate. Serve one breast with about 1 - 2 tablespoons basil sauce. Mmm good.