Place the salted butter in a large saucepan and melt it over medium-low heat.
Continue cooking while stirring constantly until the butter develops a deep amber hue and a distinctly nutty aroma, approximately 5 minutes.
Remove the saucepan from the heat and allow the browned butter to cool for 30 minutes.
While the butter cools, place the honey and kosher salt in a small bowl.
Stir thoroughly until the salt is evenly dissolved throughout the honey. Set the mixture aside.
Preheat the oven to 350°F (175°C).
Line a baking sheet with parchment paper and reserve it for the shaped cookie dough.
Once the browned butter has cooled, add the packed dark brown sugar and the prepared honey-salt mixture to the saucepan.
Blend thoroughly with a rubber spatula, scraping the bottom of the pan to incorporate all of the browned butter solids.
Add the egg yolk, vanilla extract, pumpkin purée, baking soda, and pumpkin pie spice. Stir until the mixture is smooth and uniform.
Fold in the all-purpose flour until no dry streaks remain and a cohesive cookie dough forms.
Coat every dough ball evenly in the cinnamon-sugar mixture.
Arrange the coated portions on the parchment-lined baking sheet, leaving approximately 3 inches of space between them.
Bake for 9–11 minutes, or until the cookie edges become golden.
Immediately after removing the cookies from the oven, firmly strike the baking sheet against the stovetop five times. This action encourages the tops to crack and helps create a chewier finished texture.
Leave the cookies on the baking sheet for 5 minutes.
Transfer them to a wire cooling rack and allow them to cool completely.
Finish with a light sprinkling of flaked sea salt, if desired.