Trim and remove the strings on the snap peas. Blanch peas for 20 seconds in boiling water before plunging in ice water. Drain thoroughly.
Wash, dry, and slice peach into 12-16 segments (very thin).
Combine garlic, thyme, vinegar, olive oil, and pepper.
Toss sliced peaches and peas in dressing until coated. Add shaved cheese and very gently toss. Serve within 4 hours.