Preheat oven to 375°F. Line baking sheets with parchment paper and set aside.
To brown your butter - in a large saucepan over medium-high heat, melt the butter, stirring occasionally. Once melted, begin stirring often. Butter will crackle and pop as it browns and will start to foam slightly. Once sizzling sound stops, continue stirring until golden brown bits begin to collect on the bottom of the pan. The butter will smell nutty and aromatic. Set aside in a heatproof bowl to cool.
In a medium bowl, whisk together the flour, baking soda, cream of tartar, salt and nutmeg.
In a large bowl, whisk together the browned butter, granulated sugar, brown sugar, and pumpkin until smooth. Add the egg and vanilla and whisk to combine. Add flour mixture and stir to combine, about two minutes.
In a small bowl, whisk together the granulated sugar, cinnamon, and allspice. Drop heaping tablespoons of dough into sugar mixture and roll into 1½ inch balls. Transfer to parchment paper-lined baking sheets, about 3 inch apart. Sprinkle with more sugar mixture.
Bake for 10-12 minutes, rotating sheets halfway through. Bake until golden brown and firm to the touch. Let cool for 5 minutes on sheets and then transfer to a wire rack to cool completely.