Preheat the oven to 350 degrees F. Line a few baking sheets with silicone baking mats or parchment paper. These cookies tend to stick, so I highly recommend some sort of liner instead of baking straight on the pan.

In a large bowl or stand mixer, beat the butter for about 2 minutes, until it is smooth and creamy. Scrape down the sides and bottom of the bowl to make sure there are no lumps.

Add 3/4 cup granulated sugar and 3/4 cup brown sugar. Beat 1 minute until fluffy.

Add 1 cup pumpkin puree (make sure it's not pumpkin pie filling!)

Add 1 and 1/2 teaspoons vanilla and 1 large egg. Beat until combined, scraping sides. The dough will look kind of grainy at this point.

Use a spoon to measure your flour into your measuring cup, then level off the top. Add the 2 and 1/2 cups flour to the bowl, but don't mix yet.

Make a well in the center of the flour, and add 1 teaspoon baking soda, 1 teaspoon baking powder, 3/4 teaspoon kosher salt, 1 and 1/2 teaspoons cinnamon, and 1 and 1/2 teaspoons pumpkin pie spice. Use your teaspoon to stir these ingredients into the flour a bit so you don't end up with any clumps of baking soda in your cookies.

Turn the mixer on and combine the dry and wet ingredients. Mix ONLY until combined and no more. Use a spatula to scrape the bottom of the bowl. If you see any streaks, mix it some more. Do not over mix, or your dough will be tough.

Use two spoons to drop the cookie dough onto the prepared pans. The dough is more like a batter; very wet and sticky. I tried using a cookie scoop but it just sticks too much. I scraped up a heaping tablespoon of dough with one spoon (I used a larger soup spoon) and scraped it onto the pan using another spoon. It doesn't need to be an exact ball shape. Leave about 2 inches of space in between each cookie.

Bake in the preheated oven for 12-14 minutes, or until the cookies are no longer shiny on top. Normally I under-bake my cookies to keep them chewy, but these cookies are more like tiny little pumpkin cakes; nobody wants raw batter in the center of a cake. If the shine from the top of the cookies is completely gone, take them out. They should be nice and tall and puffy.

Let the cookies cool and set up on the pan for about 5 minutes.

Transfer the cookies to a wire rack to cool completely. I always cheat and throw my cooling rack directly in the freezer to speed up the cooling process. Takes like 5 minutes, and then you can glaze right away.

To make the icing: In a small saucepan, add 3 tablespoons salted butter. Turn the heat to medium and let the butter melt. Keep the heat on medium and don't walk away. Stir occasionally. Soon the butter will bubble and form a thick white foam on top. After that, the foam will recede a little bit and you will start to see little brown "bits" forming on the bottom of the pan. Stir them up and take a whiff. If you see brown specks and your butter has taken on a nutty aroma, your butter is browned. Take it off the heat right away. The whole process doesn't take more than 3-4 minutes for this amount of butter. It goes from browned to burned real quick, so pay attention!

Place a strainer over the top of the saucepan, and add 3 cups of powdered sugar (I did it 1 cup at a time). Sift the powdered sugar into the butter. (You might be thinking "I don't have time for sifting. Sifting is for suckers." That's what I thought the first time I made this, and my icing was lumpy. No amount of whisking smoothed it out, and I ended up pressing my finished glaze through a strainer. Don't be like me.)

Once you've added all the powdered sugar, add 4 tablespoons of cream or milk. Whisk it all together until smooth. At this point you can add more powdered sugar or cream/milk, depending on the consistency you want for your glaze. If you want it to be thicker (more like frosting) add less milk/cream. You can also add a bit more powdered sugar.

Once the cookies have cooled completely, drizzle over the tops of each cookie.

These cookies don't do well stored in a tupperware, they are too moist. It's better to store them on a plate with plastic wrap loosely covering them (once the glaze has set). I'm a huge fan of warm cookies, but these ones are actually really delicious when chilled in the fridge. Try it out!