Preheat the oven to 350°F. Line rimmed baking sheets with parchment paper.
Make the batter: Combine the cake mix, pudding mix, flour, water, and oil in the bowl of a stand mixer fitted with the paddle attachment. (Or use a large bowl and an electric hand mixer.) Beat just until combined. Add the eggs and vanilla and beat until the yellow disappears. (Do not over-beat). Stir in the sprinkles.
Spoon the batter into circles onto the prepared baking sheets using a cookie scoop and spacing about 2 inches apart. Bake, in batches, 11 to 12 minutes or until golden brown and set. Remove from the oven and let cool completely in the pans.
Make the vanilla cream filling: Beat the butter in the bowl of a heavy-duty stand mixer fitted with the paddle attachment until light and fluffy. Add the marshmallow fluff and beat until creamy. Add the powdered sugar, vanilla, and salt, and beat until smooth.
Transfer the filling to a pastry bag or large zip-top plastic bag. Remove the cookies from the pan. Pipe the filling onto the flat sides of half of the cookies. Place the remaining cookies on top of the filling, flat sides down.