Preheat oven to 325°F.
Butter and flour two 8- or 9-inch round cake pans.
In a mixing bowl, whisk together the flours, baking powder, and salt. Set aside.
Cream together the butter and sugar until fluffy and pale in colour.
Beat the eggs in one at a time, fully incorporating each egg and scraping down the bowl between each addition. Beat in the vanilla.
Add about 1/3 of the milk, beat to incorporate, then 1/3 of the flour, again beating to incorporate.
Repeat this process, scraping down the bowl as necessary, until all of the milk and flour are added and mixed in evenly.
Divide the batter equally between two mixing bowls. In one, add 2 tablespoons of milk and the additional 2 tablespoons of all-purpose flour. Whisk until smooth.
In the other bowl, whisk in the cocoa powder and remaining 2 tablespoons of milk until smooth.
To create the swirls, scoop 1/3 of a cup of the white batter into the center of each prepared pan. Follow this with 1/3 of a cup of the chocolate batter directly into the center of the white batter in each pan. Repeat the process -white batter, chocolate batter, white batter, chocolate batter- each time, pouring the batter directly into the center of the contrasting batter. This will form concentric circles (and when baked, the stripey swirls) of contrasting colour. Repeat until you run out of batter.
Bake, rotating midway through, for about 35 minutes or until the cake tests done.
Let the cakes cool in the pan on a rack for 5 minutes before turning out onto the racks to finish cooling.