Preheat the oven to 355º F (180º C). Line several baking sheets with parchment paper or silicone baking mats (to prevent the cookies from sticking).
In a large bowl, with an electric mixer or hand whisk, beat the butter for 2 minutes, until smooth and creamy.
Add the white sugar and brown sugar and beat for 1 more minute or until the mixture turn fluffier. Add the pumpkin puree and mix again.
Add in the vanilla and egg and mix until everything is well combined, the mixture will look a little lumpy at this point.
In another bowl, a small one, mix together the flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg and clove powder.
Add the flour mixture to the butter mixture a little at a time, in three separate additions, beating after each addition. Only beat until the flour is combined, to avoid overbeating. The mixture will be sticky, more like batter.
Use two spoons to form balls directly on the baking sheets. Each ball should be about a tablespoon to a tablespoon and a half in quantity. Leave about 2 inches of space between each cookie, because they grow a lot during baking.
Bake the cookies for 8 to 12 minutes, just until the top of the cookies are no longer shiny, and they look dry. The idea is for the cookies to not overbake, and be very soft. Then remove them from the oven.
Let the cookies cool on the same baking sheet for 5 minutes. Then transfer them to a wire rack to cool down completely.
For the glaze or frosting:
In a small saucepan, over medium heat, melt the salted butter. Stir the butter occasionally with a rubber spatula and let it continue to cook. A kind of white foam will form on top, then this foam will disappear a little and some brown bits will form on the bottom, this is when the butter is browned, and will have a hazelnut aroma. It is necessary to stir a lot to prevent the butter from burning.
Slowly add the powdered sugar, and continue to stir with the rubber spatula, until you get the texture you like. It could be more like icing or thicker.
Once the cookies are cooled down, add a little icing or frosting on top of each one and a pinch of ground cinnamon to decorate.