In a small saucepan over medium-high heat add the balsamic vinegar and boil until it cooks down to half (about 10 minutes). The mixture should be thicker and should stick to the back of a spoon.
Add the honey to the mixture, stir to combine and remove from heat. Set aside.
In a medium bowl mix together mascarpone cheese, cream cheese, salt, pepper, and honey. Set in the fridge to chill while you prepare the peaches.
Preheat grill to medium-high heat (about 450°F)
Cut peaches in half and remove the pit. Brush the tops with olive oil and sprinkle with salt and pepper.
Lightly brush the grill grates with oil and then set the peaches cut side down on the grill grates. Grill undisturbed for 3-4 minutes (depending on grill heat) and then turn the peach 90°. Grill for an additional 3-4 minutes and then remove from heat
Using a 1" ice cream scoop or a tablespoon, scoop the cheese mixture on top of each peach, top with a drizzle of balsamic reduction, a basil leaf, and a drizzle of honey.