01 - Preheat your oven to 350°F (175°C). Prepare a 13x9-inch sheet pan by greasing it and lining it with parchment paper.
02 - In a large mixing bowl, thoroughly whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves.
03 - In a separate bowl, whisk together both sugars and the melted butter until the mixture is smooth. Incorporate the eggs, pumpkin purée, milk, and vanilla extract, whisking until all components are well combined.
04 - Gently fold the wet ingredient mixture into the dry ingredients until they are just incorporated. Exercise care to avoid overmixing the batter.
05 - In a small bowl, combine the sugar and cinnamon designated for the swirl. Stir in the melted butter until a thick paste forms.
06 - Pour half of the cake batter into the prepared sheet pan and spread it evenly. Distribute half of the cinnamon swirl mixture over the batter, then delicately swirl it into the batter using a knife or skewer. Repeat this process with the remaining batter and cinnamon swirl.
07 - Bake for 33 to 38 minutes, or until a toothpick inserted into the center of the cake emerges clean.
08 - Allow the cake to cool completely in the pan placed on a wire rack.
09 - If using, prepare the frosting by beating the softened cream cheese and butter on medium speed until smooth. Gradually add the powdered sugar, vanilla extract, and salt, beating until the mixture is light and fluffy. Spread the frosting evenly over the completely cooled cake.
10 - Slice the cake and serve.