Preheat the oven to 350°F (175°C). Line two large baking sheets with parchment paper.
Whisk the dry ingredients: in a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, cloves, and salt.
Mix the wet ingredients: in a large bowl, whisk the pumpkin purée, brown sugar, granulated sugar, eggs, oil, and vanilla until smooth and well combined.
Combine: add the dry ingredients to the wet ingredients in two additions, stirring with a spatula just until no streaks of flour remain. Do not overmix, or the cakes will turn tough.
Scoop and bake: using a medium cookie scoop (about 1 1/2 tablespoons), drop 24 evenly sized mounds onto the prepared sheets, spacing them about 2 inches apart. Smooth the tops lightly with the back of a damp spoon. Bake for 12–14 minutes, until the tops are puffed and spring back when lightly pressed. Let cool on the pan for 5 minutes, then transfer to a wire rack to cool completely.
Make the filling: beat the cream cheese and butter together on medium speed until completely smooth and creamy, about 2 minutes. Add the powdered sugar in two additions, then the vanilla and salt, beating until light and fluffy, about 2 more minutes.
Assemble: spread or pipe a generous layer of filling onto the flat side of 12 cakes. Top with the remaining cakes, flat-side down, and press gently to sandwich. Chill for 20 minutes before serving so the filling sets.