Spiced Pumpkin Shortbread Cookies

1. Add 6 tablespoons butter to a small saucepan set over medium heat. Cook until the butter begins to brown, about 3-4 minutes. Remove from the heat and transfer to a large heatproof bowl. 
2. Beat together the remaining 6 tablespoons of butter, the cooled browned butter, pumpkin butter, brown sugar, and vanilla until creamy. Add the flour and pumpkin pie spice. Mix until combined. If the dough is too sticky to form a ball, add 2-4 tablespoons of flour. 
3. Place the dough on a large piece of parchment paper. Divide in half and shape each ball into a log around 6 inches long. Chill 1-2 hours, or up to 5 days.
4. Preheat the oven to 350° F. Line a baking sheet with parchment paper. 
5. On a plate, mix the coarse sugar, cinnamon, and a pinch of salt. Unwrap the logs and place them on a cutting board. Brush with the beaten egg and roll in the coarse sugar to coat. Cut 11-12 cookies from each log.
6. Arrange the cookies on the prepared baking sheet. Bake 12-14 minutes, until the edges are golden brown. Let the cookies cool on the baking sheet. 
7. Drizzle the chocolate over each cookie and sprinkle with flaky sea salt. Enjoy a couple with that melty chocolate!