Let the butter sit at room temperature until soft enough to press easily with a finger but not melted. This helps it blend smoothly with the sugars.

In a large bowl, beat the softened butter, brown sugar, and 1/4 cup granulated sugar on medium speed for about 2 minutes, until creamy and evenly combined. The mixture does not need to become extremely fluffy.

Beat in the pumpkin puree, egg yolk, and vanilla extract until smooth. The mixture may look slightly curdled because of the pumpkin; this is normal.

In a separate bowl, whisk together the flour, cream of tartar, baking soda, 1/2 teaspoon ground cinnamon, 1/2 teaspoon pumpkin pie spice, and salt.

Add the dry mixture to the pumpkin mixture: Mix on low speed just until the flour disappears. The dough should be soft and slightly sticky. Do not continue mixing once it comes together.

Cover the bowl and refrigerate for 30 minutes. The dough should feel noticeably firmer and easier to scoop. If it is still very sticky, chill for another 10 to 15 minutes.

Heat the oven to 350°F (175°C) and line two baking sheets with parchment paper. In a small bowl, combine the 1/3 cup granulated sugar, 1 teaspoon ground cinnamon, and 1/4 teaspoon pumpkin pie spice.

Scoop the chilled dough into approximately 1-tablespoon portions: Roll each portion gently between your palms to form a small ball, then roll it thoroughly in the cinnamon-sugar mixture.

Place the coated dough balls about 2 inches (5 cm) apart on the prepared baking sheets. Avoid flattening them; they will spread slightly as they bake.

Bake for 10 to 12 minutes, one sheet at a time if your oven has uneven heat. The cookies should look puffed, with dry-looking edges and centers that are still soft. They should not develop deep brown edges.

Let the bites cool on the baking sheet for 5 minutes, then transfer them to a wire rack. The centers will firm as they cool while staying soft and tender.