Warm honey in microwave for 15 seconds. Stir in almond and vanilla extracts.
Pulse amaretti and almonds in food processor until crushed and well combined. Add butter and pulse until combined and crumbly. Preheat grill to medium.
Lightly brush cut sides of nectarines with honey mixture. Oil grill. Place nectarines on grill, cut sides down, and cook until grill marks appear, about 2 minutes. Turn over, spoon about 1/2 Tbsp. topping into each nectarine cavity and grill for about 5 minutes longer, until fruit has softened but still retains its shape. Serve immediately.