Beat the room-temperature cream cheese with confectioners' sugar and 1/2 teaspoon vanilla for 60 to 90 seconds at medium speed. Scrape the bowl once at 45 seconds. Scoop twelve level tablespoon portions onto a lined plate, then freeze them at 0°F for 35 to 40 minutes. Keep each mound slightly irregular instead of smoothing it perfectly. The mixture should look thick and satiny with no dry sugar pockets. After freezing, each portion should feel firm at the edges but still yield slightly when pressed. Pull them too early and the centers smear into the dough. Freeze until firm because cold filling melts slower than the cookie shell.

Beat softened butter with light brown sugar and 1/2 cup granulated cane sugar for 2 minutes at medium speed. Add the egg yolk, blotted pumpkin puree and remaining vanilla, then mix for 45 seconds. Fold in flour, pumpkin pie spice, cinnamon, baking soda and sea salt with a rubber spatula using broad J-shaped strokes. Chill the dough at 38°F for 30 minutes. The dough should change from glossy orange paste to a soft matte mass that holds a scoop mark. You'll smell butter and warm spice, while no dry flour streaks remain. Overmix after the flour disappears and the cookies turn tough. Chill for 30 minutes because hydrated flour supports the frozen filling.

Divide the chilled dough into twelve equal 55-gram portions. Flatten each piece into a 3 1/2-inch round, place one frozen filling mound in the center and pinch the edges closed. Roll each sealed ball between your palms for 8 to 10 seconds. Then coat it in the remaining granulated cane sugar mixed with cinnamon. Work while the filling stays below 40°F. The shaped Pumpkin Cheesecake Cookies should look plump and round with faint seams hidden underneath. The cinnamon sugar must cling in a thin uneven layer, not form wet patches. Leave a gap and the filling escapes during baking. Seal every edge because trapped filling needs a continuous dough shell.

Arrange six cookies per lined half-sheet pan with 3 inches between them. Bake one pan at a time in a 350°F preheated oven for 12 to 14 minutes. Rotate the pan 180 degrees at minute 8, then remove it when the edges look set. Let the cookies rest on the hot pan for exactly 10 minutes. The tops should puff, crack lightly and deepen from orange to golden brown around the rims. The centers will still look soft, but they shouldn't appear wet. Go past minute 14 and the filling dries while the bottoms darken. (My first batch baked at 375°F, the edges hardened before the centers settled.) Bake gently because slower heat protects the cheesecake center.

Transfer the cookies after their 10-minute pan rest and cool them at 70°F for 25 to 30 minutes. Place one cookie on a white dessert plate, then pull it apart slowly from opposite edges. Keep the remaining eleven cookies whole until serving. The filling needs time to settle before you expose the center. The split cookie should show a thick white layer with soft clean edges and no liquid seepage. The pumpkin shell should bend slightly before breaking, while cinnamon sugar stays visible on top. Split too soon and hot filling drags through the crumb. Cool fully because the cream cheese firms as its fat resets.