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Lay the apricots cut-side-down on the grill. Grill until the apricots have solid grill marks and release themselves easily from the grill, 3 to 4 minutes. If you try to remove them and they stick - let them be - they will release in time.
Transfer the apricots to a platter cut-side-up. Top the apricots with spoonfuls of the goat cheese, sprinkle with pepper and garnish with torn rosemary leaves if using. Drizzle with olive oil and sprinkle with salt if using.