Brown the butter: Place the butter in a small oven-safe baking dish and brown in a toaster oven, or brown it in a saucepan on the stovetop. Continue until the butter is bubbling and golden brown around the edges and on top. Remove from the heat and allow to cool to room temperature.
Mix the butter, sugar, honey, and salt: Add the cooled brown butter, honey, brown sugar, and salt to a mixing bowl. Mix at medium to medium-high speed until the mixture resembles wet sand.
Add the egg yolk: Add the egg yolk and continue mixing for 1–2 minutes, until the mixture becomes lighter and slightly creamy.
Add the wet ingredients: Add the sourdough starter, pumpkin puree, and vanilla extract. Mix by hand until well combined.
Add the dry ingredients: Add the flour, baking soda, pumpkin pie spice, and cinnamon. Mix by hand until a smooth dough forms.
Chill the dough: Cover and refrigerate the dough overnight, or for at least several hours. The dough can be baked the same day, but an overnight cold ferment will give the cookies more depth of flavor.
Prepare the oven: When you're ready to bake, preheat the oven to 350°F. Line a baking sheet with parchment paper.
Shape the cookies: Scoop the chilled dough into approximately 1½-2 tablespoon portions. Shape each portion into a small, thick disk about 2 inches across and ½ inch tall.
Bake: Place the cookies on the prepared baking sheet, leaving room for them to spread. Bake at 350°F for approximately 12 minutes.
Rotate and finish baking: Rotate the baking sheet 180° and continue baking for approximately 5 more minutes. Keep a close eye on the cookies because their dark color makes it difficult to judge doneness. The edges should be set while the centers remain slightly soft.
Cool: Allow the cookies to cool on the baking sheet for several minutes before transferring them to a cooling rack.
Notes
Use your favorite pumpkin spice blend. The spice ratios vary significantly between brands, so the flavor can vary from one blend to another.
Let the brown butter cool before mixing. Hot butter can affect the texture of the dough and may partially cook the egg yolk.
Cold ferment if you can. The cookies can be baked the same day, but I think the flavor is noticeably better after an overnight rest.
Don't overbake them. Because the cookies are dark, they're a little harder to judge visually. The edges should be set while the centers are still slightly soft.
Use active starter or discard. Both work beautifully in this recipe, making these a great way to use up extra starter.