Brown the Butter. Add the butter to a saucepan over medium heat. Let it melt, stirring occasionally. Once it begins to foam and turn golden, keep stirring until it develops a light nutty aroma and golden-brown color. Be careful not to let it burn. Remove it from the heat and pour it into a heat-safe mixing bowl. Let it cool until it is warm but no longer hot.
Mix the Sugars. Add the brown sugar and granulated sugar to the cooled butter. Mix until the butter and sugars are smooth and well combined.
Add the Wet Ingredients. Mix in the egg and vanilla. Add the honey and pumpkin puree, then stir until everything is evenly incorporated.
Add the Dry Ingredients. In a separate bowl, whisk together the flour, cinnamon, salt, allspice, ginger, and baking soda. Gradually add the dry ingredients to the pumpkin mixture. Mix just until a soft cookie dough forms. Avoid over mixing.
Shape the Cookies. Scoop the dough into portions of about 1½ tablespoons, or roughly 28–29 grams each. Roll each portion into a smooth ball and place them on a parchment-lined baking sheet.
Chill the Dough. Cover the cookie dough and refrigerate for at least 2 hours. You can also chill the dough overnight.
Make the Cinnamon Sugar. When you're ready to bake, combine the granulated sugar and cinnamon in a small bowl. Roll each chilled cookie dough ball in the cinnamon-sugar mixture until lightly coated.
Bake. Preheat your oven to 350°F (175°C). Place the cookies on a parchment-lined baking sheet, leaving space between each one for spreading. Bake for 10–12 minutes, or until the tops look set and the centers still appear slightly soft.
Cool. Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack. They'll continue to set as they cool while staying soft and chewy in the center.