Brush the peach halves flesh side with the basil olive oil. Place the peaches, flesh side down, on the grill or grill pan. Let cook until you have nice grill marks. About 5 minutes.
Meanwhile, in a small bowl, mix the mascarpone and sugar until well combined.
In a small saucepan, heat the balsamic vinegar over low-medium heat until boiling. Reduce heat and cook for about one minute until the vinegar is syrupy. Let cool. The vinegar will get thicker as it cools.
Plate the peach halves on a platter, flesh side up. Using a small ice cream scoop, scoop the mascarpone and top each half with one small scoop. Sprinkle with the sliced almonds and drizzle with the reduced pineapple vinegar. Sprinkle with the flaky salt and garnish with a basil leaf. Dig in and enjoy!