Preheat the oven to 350°F (175°C). Grease a 9×5-inch loaf pan and set aside.
In a large bowl, whisk together the pumpkin puree, vegetable oil, granulated sugar, brown sugar, eggs, and 1 teaspoon vanilla extract until smooth and combined.
Add the grated zucchini to the wet mixture and stir to combine.
In a separate bowl, sift together the flour, baking soda, baking powder, salt, cinnamon, nutmeg, and cloves.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
In a medium bowl, beat the softened cream cheese with 1/4 cup granulated sugar, 1 egg, and 1/2 teaspoon vanilla extract until smooth and creamy.
Pour half of the zucchini pumpkin batter into the prepared loaf pan and spread evenly.
Drop spoonfuls of the cream cheese mixture over the batter layer, then gently swirl with a knife or skewer to create a marbled effect.
Pour the remaining batter over the cream cheese layer and spread evenly.
Bake for 55 to 65 minutes, or until a toothpick inserted into the center comes out clean or with just a few moist crumbs.
Remove from the oven and let the bread cool in the pan for 15 minutes.
Transfer the bread to a wire rack and cool completely before slicing.