Whisk all dredging ingredients in a bowl to mix well
Dredge chicken slices in mixture just to lightly coat and dry chicken
Heat oil and butter in large skillet. Add prepared chicken slices and cook until golden on one side, about 2 minutes. Turn over
Add mozzarella over chicken and scatter grape tomatos around pan. Cover and cook just until chicken is cooked through and cheese melts, about 3 to 4 minutes
Remove chicken, tomatos and cheese to a serving platter. Tent with foil to keep warm while making sauce. Into skillet chicken was cooked in add chicken broth, scrape up any brown bits on pan while heating brth to a boil, cokl until just a couple of tablespoons are left. Add cream and balsamic vinegar and cook until its a sauce consistancy, about 3 minutes. Add basil and chives.
Drizzle sauce over chicken, serve any remaining sauce on the side