Preheat oven to 350°F (177°C). Grease one 12x18-inch sheet pan, two 9x12-inch sheet pans or 24 cupcake tins.
In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg and allspice.
In the bowl of an electric mixer, combine sugars, melted butter and eggs until well mixed. Gradually stir in dry ingredient mixture until combined. Stir in pumpkin puree until incorporated.
Pour batter into sheet pans or tins, filling about 3/4 inches deep. Bake for 20 to 25 minutes or until a toothpick inserted comes out clean. Cool completely on a wire rack.
While the cakes cool, make the frosting. In a medium skillet, heat the butter on low heat until melted. Stir occasionally until butter turns frothy, then stir continuously. Allow the butter to turn brown with dark specks; it will smell nutty. Remove from heat and let cool.
In the bowl of an electric mixer, combine browned butter, Bruegger’s Bagels Pumpkin Cream Cheese, bourbon, vanilla, confectioners’ sugar and heavy cream. Beat until smooth. Refrigerate for 30 minutes to firm up.
Meanwhile, prepare the push-pop containers. Cut the cake into circles. Cut the sheet cakes with a circular biscuit cutter small enough to just fit into the push-pop containers. With the biscuit cutter, cut the cake or cupcakes into small pieces. (Cupcakes may need to be sliced horizontally as well.)
Prepare a piping bag with a star nozzle and fill with frosting. To make a push pop, place one cake circle in the base of the push-pop containers. Working in a circular motion, top the cake circle with a swirl of frosting. Top with a pinch of chocolate sprinkles. Add another cake circle, frosting and more sprinkles. Repeat once more (three layers total) and top with both sprinkles and pumpkin seeds. Serve or cover with lids if not enjoying right away.