Set oven rack to lower center of oven. Preheat oven to 375 degrees F (190 degrees C). Toast walnuts on a baking sheet in the preheated oven for 5 minutes. Cool.
Whisk together the flour, sugar, baking powder, and salt in a large bowl. Toss butter pieces in the flour mixture to coat. Use a pastry blender to cut in the butter until the mixture resembles fine crumbs. Stir in toasted walnuts. Beat egg in a large bowl. Mix in the half-and-half, 1 teaspoon maple extract, and vanilla extract. Stir the dry ingredients into the wet ingredients, mixing just until blended, switching from a spoon to your hands as the mixture comes together. Place dough in 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.
Stir together the confectioners' sugar, hot water, and 1/8 teaspoon maple extract. Drizzle on scones to glaze.
