In a large bowl, whisk together the flour, cream of tarter, baking soda, salt, and pumpkin pie spice; set aside.

In the bowl of a stand mixer fitted with a paddle attachment, mix the butter and cream cheese together until smooth and creamy. Add the pumpkin, 1 cup granulated sugar, powdered sugar, egg, egg yolk, and vanilla and mix until fully incorporated. Gradually stir flour mixture into wet ingredients until dough comes together.

Place remaining 2 Tablespoons of sugar into a small bowl. Roll dough into balls about the size of a golfball and place on the baking sheet. Repeat process with more dough until you have 10 or so balls spaced at least 2 inches apart. Coat the bottom of a glass with cooking spray, dip in the sugar, and flatten each dough ball to about 1/2-inch thickness. It's okay if the cookies form a rim on the edges. Spray more cooking spray on the bottom of the glass between batches, if needed.

Bake cookies for 7-9 minutes or until tops look mostly dry around the edges, yet still glossy in the center--no browning. Remove from the oven and allow to cool on the baking sheet for 3-4 minutes before transferring to a wire rack to cool completely.

In a medium saucepan, melt the butter over medium-low heat. As the butter melts, it'll start to foam, then turn a clear golden color. Continue to stir the butter, scraping up any browned specks from the bottom of the pan as it starts to brown. It should have a nutty aroma.

Once browned, pour butter into a shallow bowl and place in the freezer for about 30 minutes, or until it's solid and thoroughly chilled.

Scrape the butter out into the bowl of a stand mixer fitted with the paddle attachment and beat for about 1 minute until lightened up and creamy. Add the sour cream, vanilla, salt, and 2 1/2 cups of the powdered sugar and beat for about 3 minutes until smooth.

Add cream cheese, one piece at a time, mixing well after each addition to prevent any lumps. Add the remaining 1 cup of powdered sugar, and beat for about 2 minutes until fluffy.

Spread frosting onto cooled cookies. Allow frosting to set (dry) before stacking or covering in plastic wrap. Store cookies in an airtight container for up to one week.