Set oven rack to lower center of oven. Preheat the oven to 375 degrees F (190 degrees C). Toast walnuts on a baking sheet in the oven for 3 to 5 minutes. Cool.

Whisk together flour, sugar, baking powder, and salt in a large bowl. Toss butter pieces in flour mixture to coat. Use a pastry blender to cut in butter until mixture resembles fine crumbs. Stir in toasted walnuts.

Beat egg in a large bowl. Mix in half-and-half, maple extract, and vanilla extract. Stir dry ingredients into wet ingredients, mixing until just blended, switching from a spoon to your hands as mixture comes together. Place dough in the refrigerator for 10 minutes.

Roll chilled dough into a ball on a lightly floured surface. Flatten dough into a 3/4-inch circle. Cut into 8 wedges.

Bake scones on a parchment-lined baking sheet just until firm and the bottoms are lightly browned, 15 to 20 minutes. Cool for 3 minutes before transferring to cooling racks.