Place the 1/2 cup (113 g) pumpkin purée in a small microwave-safe bowl. Microwave uncovered on high power for 1 minute, then stir thoroughly. Continue heating in 1-minute intervals, stirring between each, for approximately 4 to 5 minutes total. The pumpkin should darken slightly, become noticeably thicker, and reduce to approximately 1/4 cup (57 g). This evaporation removes excess moisture. Let the reduced purée cool for 15 minutes before mixing it into the dough.
Add the 12 tablespoons (170 g) softened unsalted butter and 1 1/2 cups (297 g) granulated sugar to a large mixing bowl. Beat with an electric mixer on medium speed for 1 to 2 minutes, until the mixture looks lighter, creamy, and slightly fluffy. This incorporates air and distributes the fat evenly through the sugar.
Add the cooled, reduced pumpkin purée to the butter mixture and beat until evenly incorporated. Add the 2 large eggs and 2 teaspoons (10 mL) vanilla extract. Mix on medium-low speed for approximately 1 minute, scraping the bowl as needed. The mixture should look thick and mostly uniform. Small variations in texture are normal because pumpkin contains moisture.
In a medium mixing bowl, whisk together the 3 cups (360 g) all-purpose flour, 2 1/2 teaspoons (approximately 6 g) pumpkin pie spice, 1 1/4 teaspoons (approximately 7.5 g) fine table salt, 1 teaspoon (approximately 5 g) baking soda, and 1 teaspoon (approximately 3 g) cream of tartar. Mix for approximately 30 seconds until the spices and leavening are evenly distributed. Add the dry mixture to the wet ingredients and mix on low speed just until no visible flour remains. Stop mixing once the dough looks cohesive to avoid excessive gluten development.
Cover the mixing bowl and refrigerate the dough for at least 60 minutes. The butter will firm up and the flour will absorb moisture, reducing excessive spreading during baking. The chilled dough should feel firm enough to scoop and roll without flowing or sticking heavily to your hands.
Preheat the oven to 350°F (177°C), positioning racks in the upper and lower thirds. Line the 2 large baking sheets with parchment paper. Let the chilled dough stand at room temperature for approximately 10 minutes to make scooping easier. Meanwhile, combine the 1/4 cup plus 2 tablespoons (74 g) granulated sugar, 1 tablespoon plus 1/2 teaspoon (approximately 9 g) pumpkin pie spice, and 1 pinch (approximately 0.3 g) fine table salt in a shallow bowl. Stir until the coating is uniformly colored.
Scoop the dough into approximately 2-tablespoon (30 mL) portions, weighing about 36 g each, and roll into smooth balls. Roll every portion in the spiced-sugar mixture until fully coated. Arrange approximately 13 cookies on each prepared baking sheet, leaving at least 2 inches (5 cm) between them. Distribute any remaining coating over the tops. Keep the dough balls rounded to encourage thicker centers as the cookies spread.
Bake at 350°F (177°C) for 12 to 15 minutes, switching the baking sheets between racks and rotating them front to back halfway through. The cookies should look slightly domed with set, golden-brown edges and softer centers. Remove them before the centers become firm; residual heat will continue setting the interior during cooling.
Leave the cookies on their baking sheets for approximately 15 minutes, until they become firm enough to lift without breaking. The centers will settle slightly, and small cracks may become more visible as the cookies cool. Transfer to a cooling rack and allow them to reach room temperature before storing. This resting period lets the crumb stabilize while preserving a tender center.