Heat your oven to 350 degrees F. Grease a 9x5 loaf pan well with butter or nonstick spray, then line the bottom with a strip of parchment paper and grease that too. This makes unmolding clean and easy.

In a large bowl, whisk together the flour, baking soda, salt, cinnamon, cloves, and allspice until evenly combined. Set aside.

In the same large bowl after clearing a space, or in a second bowl, whisk the melted butter, brown sugar, molasses, eggs, milk, vanilla, and fresh grated ginger together until smooth and fully combined. The mixture will look dark and glossy.

Pour the wet ingredients into the dry ingredients and stir gently with a rubber spatula until just combined. A few small lumps are fine. Do not overmix or the loaf will be tough.

Pour the batter into the prepared pan and smooth the top with your spatula. Bake on the center rack for 50 to 55 minutes. At the 40 minute mark, check the top. If it is browning quickly, lay a loose sheet of foil over the top without crimping it down, and continue baking.

The loaf is done when a toothpick inserted into the center comes out with just a few moist crumbs, not wet batter. The top will spring back lightly when pressed. Remove from the oven and let cool in the pan on a wire rack for 15 minutes, then turn out and cool completely on the rack. Do not frost a warm loaf.

While the loaf cools, make the frosting. Beat the softened cream cheese and softened butter together with a hand mixer on medium speed for 2 minutes until fluffy. Add the sifted powdered sugar, lemon juice, lemon zest, and salt. Beat on low to start, then increase to medium-high and beat for 1 more minute until smooth and creamy.

Once the loaf is completely cool, spread the lemon cream cheese frosting evenly over the top. For clean slices, refrigerate the frosted loaf for at least 1 hour before cutting. Use a sharp knife wiped clean between cuts.