Chill your tools. Place a mixing bowl and your cubed butter in the freezer for 10 minutes. Cold ingredients keep the scones flaky.
Preheat and prep. Preheat oven to 400°F (200°C).
Line a baking sheet with parchment paper.
Mix dry ingredients. In the chilled bowl, whisk flour, sugar, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger.
Cut in butter. Add the cold butter cubes. Use a pastry cutter or your fingertips to cut the butter into the flour until pea-sized bits remain. You should still see some visible pieces of butter.
Combine wet ingredients. In a separate bowl, whisk pumpkin puree, sourdough discard, egg, vanilla, and 2 tablespoons cream or milk until smooth.
Bring the dough together. Pour the wet mixture into the dry ingredients.
Stir with a spatula until shaggy. If the mixture looks dry or floury, add the remaining 1 tablespoon cream, a little at a time. The dough should be slightly sticky but workable.
Add optional mix-ins. Fold in nuts or chocolate chips if using.
Don’t overmix.
Shape. Turn the dough out onto a lightly floured surface. Gently pat it into a 7–8 inch round, about 1 inch thick. Use a bench scraper or knife to cut into 8 wedges.
Chill the wedges. Transfer to the prepared baking sheet.
Brush tops lightly with milk or cream and sprinkle with coarse sugar if you like. Place the sheet in the fridge for 15 minutes (or freezer for 10) to firm up. Cold dough rises better and spreads less.
Bake. Bake 16–20 minutes, until the edges are golden and the centers feel set. A toothpick should come out mostly clean.
Cool and glaze. Let scones cool on the sheet for 5 minutes, then move to a rack.
If glazing, whisk powdered sugar, milk, and vanilla to a drizzle-able consistency and spoon over warm scones.