Preheat the oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan.
In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, nutmeg, cloves, and ginger until well combined.
In a large bowl, beat the softened butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the pumpkin puree, milk, and vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 55 to 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the bread from the oven and let it cool in the pan for 15 minutes.
Transfer the bread to a wire rack to cool completely before icing.
To make the icing, beat the cream cheese and butter together in a medium bowl until smooth and creamy.
Add the powdered sugar and vanilla extract and beat until combined.
Gradually add the milk, one tablespoon at a time, until the icing reaches a spreadable consistency.
Spread the icing evenly over the cooled pumpkin bread.
Slice and serve.