Preheat the oven to 400°F and line a baking sheet with parchment paper.
Make 5 to 6 slits in each chicken breast, spaced about ½-inch apart, being careful not to cut through completely.
In a small bowl, combine oil, Italian seasoning, paprika, salt, and pepper. Mix well.
Brush the seasoning mixture all over the chicken, including inside the slits.
Insert a slice of cheese and a half slice of tomato into each slit.
Bake for 25-30 minutes, or until the chicken reaches an internal temperature of 165°F.
While the chicken cooks, prepare the balsamic reduction: Boil the balsamic vinegar in a small saucepan, then reduce heat and simmer until halved in volume, stirring occasionally. Remove from heat and mix in the honey.
Serve the chicken topped with fresh basil and drizzled with the balsamic reduction.