Line 2 baking sheets with parchment paper.

Preheat a cast-iron grill pan over medium-high heat. Brush grill pan with vegetable oil. Working in batches, add nectarines to pan, and cook until grill marks form, 3 to 5 minutes per side, oiling pan as needed. Transfer to a prepared baking sheet, and let cool completely.

In a large bowl, whisk together flour, sugar, baking powder, salt, ginger, and nutmeg. Using a pastry blender or 2 forks, cut in cold butter until mixture resembles coarse crumbs.

In a small bowl, stir together cold cream and vanilla bean paste. Gradually add cream mixture to flour mixture, stirring with a fork just until dry ingredients are moistened. (Dough will be quite crumbly or shaggy in parts.)

Turn out dough onto a clean surface; gently knead until dough comes together, 8 to 10 times. On a very lightly floured surface, shape dough into a smooth 7-inch disk (about 1 inch thick). Using a bench scraper or a thin-bladed knife, cut into 6 wedges, and place ½ inch apart in a circle on remaining prepared pan. Freeze until firm, about 15 minutes.

Preheat oven to 375°F (190°C).

Bake until lightly golden and a wooden pick inserted in center comes out clean, 25 to 30 minutes. Let cool on pan for 5 minutes. Remove from pan, and let cool completely on a wire rack.

Place scones on serving platter, and top with Vanilla Bean Cream and grilled nectarines. Garnish with mint, if desired. Serve immediately.