Blot the pumpkin: spread the pumpkin puree on a plate lined with folded paper towels and press with more towels until very little moisture transfers. The puree will reduce by about a third — this step is what keeps the cookies chewy instead of cakey.
Whisk the dry ingredients: in a medium bowl, whisk together the flour, baking soda, baking powder, salt, pumpkin pie spice, and cinnamon.
Whisk the wet ingredients: in a large bowl, whisk the melted butter with the granulated sugar and brown sugar until smooth, about 1 minute. Whisk in the blotted pumpkin puree, egg yolk, and vanilla until evenly combined.
Combine: add the dry ingredients in two additions, stirring with a spatula just until no flour streaks remain. Fold in 1 1/4 cups chocolate chips. Do not overmix.
Chill the dough: cover and refrigerate for 30 minutes (up to overnight). Chilled dough scoops cleanly and bakes thick instead of spreading flat.
Scoop and top: scoop 2-tablespoon balls of dough and place 2 inches apart on parchment-lined baking sheets. Press a few of the reserved chocolate chips onto the tops of each cookie.
Bake: bake at 350°F for 11 to 13 minutes, until the edges are set and the centers still look slightly soft and puffy. Do not overbake — the cookies set as they cool.
Finish and cool: sprinkle with flaky sea salt while warm, if using. Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.