Spray a 15x10 1⁄2-inch rimmed baking sheet with baking spray with flour. Line with parchment paper, and spray again.
In a large mixing bowl, beat butter at medium speed with a mixer until creamy, 1 to 2 minutes. Beat in brown sugar until light and fluffy, approximately 3 minutes. Beat in egg until well combined. Beat in pumpkin purée and vanilla extract until incorporated. (Batter will look broken, but it will come together.)
In a medium bowl, whisk together flour, baking powder, salt, cinnamon, cardamom, ginger, baking soda, and cloves until well combined. With mixer at low speed, add to butter mixture in thirds, alternately with buttermilk, beginning and ending with flour mixture. Fold in chopped chocolate. Spread batter into prepared baking sheet. Tap baking sheet on countertop to remove air bubbles.
Bake until a wooden pick inserted into the center comes out clean, 12 to 15 minutes. Let cool completely in baking sheet on a wire rack.
Remove cake from baking sheet, and place on a cutting board. Cut cake into 2 (10 1⁄2x7 1⁄2-inch) portions.
Place1⁄2 cup Cream Cheese Frosting in a piping bag fitted with a large, fluted piping tip (Wilton #21). Set aside.
Using an offset spatula, spread half of remaining frosting onto a cake portion. Top with remaining cake portion. Spread remaining half of frosting in a smooth layer onto top of cake stack. Freeze assembled cake until firm enough to cut cleanly, approximately 1 hour.
Using a long, sharp knife, trim rough edges (approximately 1⁄4 inch) from all sides of cake, pressing downward with knife to create clean cuts and wiping knife between each cut. Cut cake evenly into 9 (approximately 2 1⁄2x2-inch) rectangles. Place cake rectangles on a serving platter.
Pipe reserved 1⁄2 cup frosting onto tops of cake rectangles in 3 rows using a shell pattern.
Let come to room temperature before serving.
Recipe by TeaTime Magazine at https://teatimemagazine.com/pumpkin-spice-layer-cakes/