Make whipped cream: in a stand mixer fitted with a whisk attachment, combine heavy cream, honey, and vanilla. Start mixer on low and gradually increase speed to high, whipping the cream until thick and soft peaks form. Cover with plastic and chill until ready to serve.
Prepare fruit: Wash and cut the peaches or nectarines in half and remove the pit. Brush the cut-side with oil.
Place fruit cut-side down on a preheated 350 degree Fahrenheit grill. Cook for 4 minutes, flip, and cook another 4 minutes or until fruit has softened and has grill marks.
Serve a half a peach topped with a scoop of vanilla ice cream, whipped cream, and crushed Amaretti cookies or mini-sized hazelnut biscotti.
For a vegan alternative, instead of whipped cream use So Delicious coconut milk whipped topping and a vegan cookie, like Nature's Path vanilla sandwich cookies. A list of other vegan cookie options can be found on peta2.com (21 Vegan Cookies You NEED to Buy).