Add butter to a light-colored saucepan over medium heat and stir constantly until the milk solids turn deep golden brown and the butter smells nutty, approximately 5–7 minutes, then immediately pour into a medium bowl (including every brown speck) to stop cooking and cool completely, about 25–30 minutes.
While butter cools, spread pumpkin purée in a thin layer onto three stacked paper towels, fold over, press firmly for 10 seconds, discard wet outer layers, and repeat with fresh towels two more times to remove excess moisture; set aside.
Add brown sugar and granulated cane sugar to the cooled brown butter and stir vigorously with a silicone spatula until the mixture looks thick, dark, and glossy with no visible dry sugar, about 30–40 strokes.
Add the whole egg and stir 20–25 strokes until fully incorporated, then add the egg yolk and stir 20 more strokes until the mixture is smooth.
Add the dried pumpkin purée and vanilla extract and stir 25–30 strokes until no orange streaks remain and the mixture looks uniformly smooth and slightly glossy.
In a separate bowl, whisk together the flour, cinnamon, ginger, nutmeg, cloves, baking soda, and salt until evenly combined.
Add the dry ingredients to the wet mixture all at once and fold with the spatula using slow upward strokes — count 20 strokes, check for dry flour, fold 5 more if needed — stop the moment all flour disappears; do not overmix.
Fold in 1¼ cups (213g) of the chocolate chips with 8–10 strokes until evenly distributed throughout the dough.
Preheat oven to 350°F (175°C) and line a light-colored aluminum baking sheet with parchment paper.
Scoop 2 tablespoons (45g) of dough per cookie, space at least 2 inches apart on the prepared sheet, and press 4–6 reserved chocolate chips onto the top of each ball.
Optional: refrigerate portioned dough balls on the pan for 30 minutes before baking for taller, slightly more defined cookies.
Bake on the middle rack at 350°F (175°C) for 11–13 minutes, until the edges look set and slightly matte and the centers still look slightly puffy and underdone.
Leave cookies on the hot pan for exactly 5 minutes without moving them, then transfer to a wire rack and cool for at least 10 minutes before eating.
