Brown the butter: Melt the butter in a light-colored saucepan over medium heat, swirling often. Watch for the foam to settle and small brown specks to form, about 5 to 7 minutes, then pour into a bowl to cool.
Cool the butter: Let the browned butter cool for about 15 minutes at room temperature. It should still be liquid but no longer hot to the touch.
Mix wet ingredients: Whisk the cooled butter with both sugars, pumpkin puree, egg yolk and vanilla extract until the mixture looks smooth and slightly glossy.
Add dry ingredients: Stir in the flour, cream of tartar, baking soda, salt and pumpkin pie spice. Mix just until no dry streaks remain; the dough will be thick.
Chill the dough: Cover and refrigerate the dough for 30 minutes, until it firms up enough to scoop without sticking to your hands.
Preheat the oven: While the dough chills, preheat your oven to 350°F and line two baking sheets with parchment paper.
Make the coating: Stir together the 1/4 cup granulated sugar and 1 tablespoon ground cinnamon in a small bowl for rolling the dough balls.
Shape and coat: Scoop the dough into 1.5-tablespoon balls and roll each one in the cinnamon-sugar mixture until fully coated.
Arrange on sheets: Place the coated dough balls about 2 inches apart on the prepared baking sheets to allow room for spreading.
Bake until set: Bake for 10 to 12 minutes, until the edges look set but the centers still look slightly soft and underbaked.
Cool on the sheet: Let the cookies rest on the hot baking sheet for 5 minutes; they will continue to firm up during this time.
Transfer and finish cooling: Move the cookies to a wire rack to finish cooling completely before storing them.