Add softened butter to a large mixing bowl and cream with a mixer for 1 minute.
Add sugar, brown sugar and vanilla and beat for 1 more minute. Add pumpkin and mix once more.
Set your sifter over something that will catch fall out and add dry ingredients. Use a spoon to briefly stir, then sift over butter and sugar ingredients, to combine.
Mix until incorporated, being careful not to over mix. Then add almond milk and mix until a soft dough is formed. Freeze dough for 15-30 minutes (or until cold), or refrigerate for 30-45 minutes (or chill overnight), preheat your oven to 350 degrees F (176 C), and position a rack in the center of the oven.
Scoop out heaping 1 Tbsp amounts of dough and roll into balls. Place on a clean baking sheet 2 inches apart to allow for spreading. Dip a glass into cane sugar and then gently smash the cookie ball down into a disc (see photo). If you find the dough is sticking to the glass, you can dip it in flour, then sugar, before smashing.
Bake on the center rack for 10-12 minutes or very slightly golden brown.
Let rest on pan for a few minutes. Then transfer to a cooling rack to cool completely. Prepare frosting in the meantime.
FOR FROSTING: Wipe/rinse your mixing bowl clean and add softened butter. Beat until light and fluffy. Then add vanilla, spices, and pumpkin butter (optional) and mix once more.
Add powdered sugar 1/2 cup at a time and continue mixing until thick and creamy. Drizzle in a little non-dairy milk to thin. You want this frosting to be pretty thick so it will hold its shape once on the cookies, so only add a little milk and add more powdered sugar if it gets too thin.
Once cooled, frost cookies and top with a sprinkle of pumpkin pie spice or cinnamon. Store leftovers covered at room temperature for up to a few days. Freeze for longer-term storage.
*Vegan butter sticks are best for baking, as the tubs can often contain water to ease spreading, which can affect the final product. I prefer Earth Balance buttery sticks for baking. *If you are trying to speed-soften your butter, simply cut it into thin slices from the stick and it will soften much quicker. *Pumpkin butter can be subbed for pumpkin puree, but hold back 1 Tbsp (amount as original recipe is written // adjust if altering batch size) of cane sugar. *Loosely adapted from my Vegan Funfetti Cupcakes! *Nutrition information is a rough estimate calculated without optional frosting.