Preheat oven to 350℉ degrees. Grease a 9 x 5-inch loaf pan.
Sift the flour, baking soda, baking powder, salt, cinnamon, ground ginger, ground nutmeg, ground cloves, and ground allspice into a medium bowl.
In a large bowl, beat the sugar, pumpkin puree, vegetable oil, eggs, and vanilla together.
Add the flour mixture to the pumpkin mixture and stir just until smooth.
Pour into the prepared loaf pan and spread evenly.
Bake for about 1 hour or until a toothpick inserted in the center comes out clean.
Let cool in the pan on a rack for 10 minutes, then turn out onto the rack to cool completely.
Add the room temperature cream cheese and butter to a large mixing bowl. Beat on medium speed until the butter and cream cheese are fluffy and well combined.
Pour in the vanilla extract, powdered sugar, and 1 teaspoon milk. Beat the icing for pumpkin bread until smooth and well combined. If needed, add more milk for a glaze-like consistency.
Spread the cream cheese frosting on the completely cooled pumpkin spice bread. Slice and enjoy!