Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper. Set them aside while you prepare the cookie dough.
Melt the butter in a light-colored skillet over medium heat, stirring frequently. Continue cooking as the butter foams and the milk solids turn golden brown, releasing a rich, nutty aroma. Remove it from the heat immediately and transfer it to a heat-safe bowl, scraping in all the flavorful brown bits. Let the butter cool until it is no longer hot.
Place the pumpkin puree in a small saucepan over medium heat. Cook for 10–15 minutes, stirring regularly, until it thickens and loses much of its excess moisture. Transfer it to a bowl and let it cool completely before using.
Combine the cooled brown butter, brown sugar, and granulated sugar in a large mixing bowl. Whisk until smooth and well combined. Add the egg, egg yolk, and vanilla extract, then mix until the mixture looks glossy and uniform.
In a separate bowl, whisk together the flour, baking soda, cinnamon, nutmeg, allspice, cloves, and salt. Add the dry ingredients to the wet mixture and stir gently until no dry flour remains. Fold in about 1¼ cups of the chocolate chips, reserving the rest for the cookie tops.
Cover the dough and refrigerate for 30 minutes, or until firm enough to scoop. Chilling helps control spreading and allows the brown butter and warm spices to develop their flavor.
Scoop the dough into portions of approximately 1½ tablespoons and arrange them on the prepared baking sheets, leaving about 2 inches between each cookie. Gently press a few of the reserved chocolate chips onto the tops for a bakery-style finish.
Bake for 10–12 minutes, or until the edges are lightly golden and the centers still look slightly soft. Avoid overbaking, as the cookies will continue to set on the baking sheet after coming out of the oven.
Let the cookies rest on the baking sheet for 5–10 minutes before transferring them to a wire rack to cool. Enjoy them slightly warm, when the chocolate is still soft and melty.