Liberally butter two 7-inch cake pans and dust with flour. Tap out the excess flour. In a medium saucepan over medium heat, stir together 1/2 cup plus 2 tablespoons stout beer and 3/4 cup dark molasses, bringing to a boil. Whisk in 1/2 teaspoon baking soda — be careful and whisk constantly, as the mixture will foam up when ou add the soda! Remove immediately from heat and let the mixture cool to room temperature.
Preheat the oven to 350 (F).
Sift together 1 1/4 cups all-purpose flour, 1 teaspoon baking powder, 1 tablespoon plus 2 teaspoons ground ginger, 3/4 teaspoon ground cinnamon, 1/4 teaspoon ground cloves, 1/4 teaspoon ground nutmeg, 1/8 teaspoon ground cardamom, and 1/4 teaspoon kosher salt. Set aside.
In the bowl of a stand mixer fitted with a whisk attachment, combine 2 eggs, 3/4 cup granulated sugar, and 1/2 cup brown sugar. Whisk on medium speed until well combined and lightened in color, about 3 to 4 minutes. Once the sugar and egg mixture has lightened, slowly drizzle in 1/2 cup vegetable oil and beat until combined.
Once the oil has been combined, reduce the mixer speed to its lowest setting and slowly add the stout and molasses mixture (from the second step). Once the stout and molasses mixture has been added completely, stop the mixer and use a rubber spatula to scape down the sides of the bowl.
Turn the mixer back on to its lowest speed and slowly add the dry ingredients (the flour and spice mixture from the fourth step), beating until just combined.
Remove the bowl from the mixer and scrape down the sides with a rubber spatula, and fold the batter by hand a few more times with the spatula. Strain the batter through a medium-mesh sieve into a clean bowl, and divide it between the prepared pans.
Bake until nicely risen and lightly browned at the edges, about 45 to 50 minutes for the cakes. Transfer to a wire cooling rack and let cool in the pans for about 20 minutes. Run an offset spatula around the edges of the pans, then invert the cakes onto the racks and let cool for another 20 minutes.
When the cakes are completely cooled, top off with cream cheese frosting (recipe follows).