Preheat the oven to 425 degrees F (220 degrees C). Line a baking sheet with parchment paper.

Combine flour, 1/4 cup plus 3 tablespoons sugar, baking powder, salt, cinnamon, nutmeg, cloves, and ginger in the bowl of a stand mixer. Mix using the paddle attachment. Add butter to the bowl and toss using a spatula to ensure butter is coated in flour mixture. Mix until mixture resembles cornmeal with butter pieces no bigger than a pea, about 2 minutes.

Whisk pumpkin, egg, and half-and-half together in a bowl until blended. Fold pumpkin mixture into flour mixture until dough can be formed into a ball.

Turn dough out onto a lightly floured surface press with your hands into a long rectangle, 3/4- to 1-inch thick. Use a pizza cutter to cut dough into 4 rectangles. Cut each rectangle into 2 triangles. Place dough triangles onto the prepared baking sheet.

Bake in the preheated oven until scones begin to brown around the edges and on top, about 15 minutes.

Transfer scones to a wire rack to cool completely, about 20 minutes.

Mix powdered sugar and milk together in a small bowl, using more sugar or more milk to reach the desired consistency. Use a brush to spread glaze on the cooled scones. Allow to harden, about 10 minutes.

Meanwhile, mix powdered sugar, milk, cinnamon, nutmeg, ginger, and cloves together in a small bowl. Drizzle spiced glaze over the first glaze and allow to harden completely, about 10 minutes more.