Preheat the oven to 350°F (175°C). Grease and flour a 9×5 inch loaf pan.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, salt, ground cinnamon, ground nutmeg, ground cloves, and ground ginger. Set aside.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy, about 3-4 minutes using an electric mixer.
Add the eggs one at a time, beating well after each addition.
Mix in the canned pumpkin puree, milk, and vanilla extract until fully combined.
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 in the preheated oven for 55-60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the bread from the oven and allow it to cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before icing.
To prepare the icing, beat the softened cream cheese and softened butter together in a medium bowl until smooth and creamy.
Add the powdered sugar, vanilla extract, and milk. Beat until the icing is smooth and spreadable. Add more milk if needed to reach desired consistency.
Once the pumpkin bread is completely cooled, spread the cream cheese icing evenly over the top.
Slice and serve.