Simmer balsamic vinegar, honey, garlic, and salt in a small saucepan for 3 to 4 minutes until reduced by half and glossy. Remove from heat. Cool.
Halve and pit peaches. Brush cut faces with olive oil and honey. Season with salt and pepper.
Preheat grill or grill pan to high heat.
Place peaches cut-side down on hot grill. Cook undisturbed for 3 to 4 minutes until deep char marks form.
Flip onto skin side. Grill a further 2 minutes until skin blisters. Remove from grill.
Dress rocket with olive oil, lemon juice, and a pinch of salt. Toss gently.
Arrange dressed rocket across a large serving platter in a loose mound.
Place grilled peach halves across the rocket.
Tear burrata apart with hands and place pieces between the peaches. Allow interior cream to spill naturally.
Scatter toasted nuts and torn basil across the platter.
Drizzle honey balsamic glaze in a sweeping stream across everything.
Finish with flaky sea salt and cracked black pepper. Serve immediately.