For the cookies: Adjust oven racks to upper-middle and lower-middle position and heat oven to 375 degrees. Line 2 large (18 by 12-inch) baking sheets with parchment paper.
Stir pumpkin, eggs, oil, sugar, vanilla, cinnamon, and nutmeg together in large bowl until well blended. Whisk flour, baking powder, baking soda, and salt together in medium bowl. Stir dry ingredients into pumpkin mixture until well incorporated.
Using small ice cream scoop (#30 is the perfect size) or tablespoon measure, drop 2 tablespoons of dough on prepared baking sheet. Spread dough into 2-inch rounds about 1/2 inch thick and spaced 2 inches apart. Bake until cookies are just set and bottoms are lightly browned, 10 to 14 minutes, rotating baking sheets from front to back and top to bottom halfway through baking. Slide cookies, still on parchment, to cooling racks. Cool baking sheets, line with fresh parchment paper, and repeat with remaining dough.
For the filling: With electric mixer, beat butter and cream cheese at medium speed until no lumps remain, about 30 seconds. Scrape down sides of bowl with rubber spatula. Add Marshmallow Fluff and beat at medium speed until incorporated, about 60 seconds. Beat in salt and vanilla until well blended, about 30 seconds. Scrape down bowl. Reduce speed to low and gradually add confectioners’ sugar, beating until smooth, about 1 minute.
Spread 2 tablespoons filling on center of flat side of one cookie. Place flat side of second cookie on filling and press cookies together to bring filling to edges. Repeat with remaining cookies and filling. (Cookies can be refrigerated in airtight container for up to 4 days).