Preheat oven to 350 degrees F. Line a large cookie sheet with parchment paper or foil. Lightly grease foil, if using. Set cookie sheet aside.
In a large bowl beat shortening with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar, brown sugar, baking soda, pumpkin pie spice, and salt. Beat until combined, scraping bowl occasionally. Beat in egg and vanilla until combined. Alternately add flour and milk, beating on low speed after each addition just until mixture is combined.
Spoon batter in 2-inch-diameter rounds about 1/2-inch high onto prepared cookie sheet, leaving 2 inches between each dough round. Bake for 9 to 11 minutes or until tops are set. Cool on cookie sheet for 2 minutes. Transfer cookies to a wire rack; let cool.
4. Spread 1 rounded tablespoon of Pumpkin-Ricotta Filling on bottoms of half of the cookies. Top with remaining cookies, bottom sides down. Drizzle or spread with White Chocolate Glaze and sprinkle with nuts. Chill until glaze is set.
Place whipping cream in a small microwave-safe bowl. Microwave, uncovered, on 50 percent power (medium) for 30 to 40 seconds or until cream comes to boiling. Add white chocolate. Do not stir. Let stand for 5 minutes. Stir until chocolate melts. Let stand for 5 to 15 minutes more before using. The glaze will firm as it stands. If you want a glaze that runs down the sides of the cookies, let glaze stand only 5 minutes; if you want glaze that spreads like thin frosting, let glaze stand for 15 minutes.
In a large bowl whisk together powdered sugar, pumpkin, mascarpone cheese, ricotta cheese, and pumpkin pie spice until smooth. Stir in pistachio nuts. Cover and chill for 1 hour.