Whisk together the salsa macha and honey in a small bowl and let sit at room temperature for 1 hour to allow the flavors to meld.
Whisk together the olive oil, vinegar and salt in a small bowl. Set aside.
Prepare the grill for direct grilling over a hot charcoal fire.
Grill the peach slices on both sides until golden brown and caramelized, about 2 minutes per side. Remove to a sheet pan.
Place the burrata on a platter and arrange the grilled peaches around it. Crack open the burrata, drizzle with the honey and vinaigrette, and garnish with basil leaves. Serve while the peaches are still warm.