Heat the oven to 350 °F and line two baking sheets with parchment paper. The parchment keeps the sugar coating from sticking and helps the bottoms bake evenly.
Spread the canned pumpkin puree over a plate and press it gently with paper towels, replacing the towels and repeating at least four more times. It should shrink from 1/2 cup to about 1/4 cup and leave very little moisture on a fresh towel.
Whisk the flour, pumpkin pie spice, baking soda, baking powder, and salt in a small bowl. Break up any visible spice clumps so the dough bakes with even flavor and lift.
Beat the softened butter and brown sugar in a large bowl with an electric mixer on high speed for 1 to 2 minutes. Stop when the mixture looks lighter in color and fluffy rather than grainy and dense.
Add the egg yolks and vanilla, then beat on medium speed for 1 to 2 minutes. The mixture should become pale, smooth, and noticeably airy.
Mix in the blotted pumpkin puree on medium-low speed. Blend only until the pumpkin is fully incorporated and no orange streaks remain.
Add the flour mixture and mix on low speed until the dough just comes together. Stop as soon as the dry flour disappears to keep the cookies tender.
Portion the dough with a 2 tbsp cookie scoop, roll each portion into a ball, and coat it in the spiced sugar. If the dough feels too sticky to shape cleanly, chill it for 10 minutes before rolling.
Arrange the coated dough balls on the prepared baking sheets with at least 2 inches between them. The spacing gives each cookie room to spread without joining its neighbor.
Bake for 12 to 14 minutes. At 12 minutes, the centers stay especially chewy; at 14 minutes, the edges become a little crisper while the centers remain puffy.
Leave the cookies on the baking sheets for 5 minutes, then transfer them to a wire rack and cool for at least 15 minutes. The puffy centers will settle and form the signature wrinkled surface as the cookies cool.