Whisk together in a bowl the flour, baking powder and salt. Set aside.
Whisk together in a separate bowl the eggs and the sugar until the mixture thickens slightly and takes on a pale yellow color. This could take a few minutes. If you’re feeling lazy, use an electric mixer for this step.
Whisk the oil and vanilla into the egg mixture until fully combined.
Pour the dry ingredients over the egg mixture. Using a rubber spatula, fold/stir just until the dry ingredients are no longer visible. Hold on to that bowl that had the dry ingredients.
Pour approximately ⅓ to ¼ of the dough into the empty bowl that had your dry ingredients. Using your rubber spatula, mix in the cocoa powder and milk just until fully incorporated.
Cover both bowls with plastic wrap and refrigerate at least two hours and up to overnight. (Can you skip this step? Sure. The dough may be a bit more difficult to work with though.)
Preheat your oven to 350°F.
Line two baking sheets with parchment paper.
Divide the vanilla portion of the dough into 4 logs, shaping each log approximately 2-3 inches wide, and place two on each baking sheet. (Tip: If the dough is too sticky, lightly wet your hands prior to handling the dough. This is a very sticky dough, and the water will make your life much easier to shape the dough. Alternatively, you can lightly flour your hands. I prefer to use water because I would rather add moisture to the dough rather than make it drier with flour.) Divide the chocolate dough into quarters and mold each quarter into a log the length of the vanilla dough. (The chocolate dough will be slightly easier to work with because the cocoa powder will have absorbed some of the moisture from the dough.) Place the chocolate logs in the centers of the two vanilla logs, or place over the vanilla dough in a zigzag. With wet hands, shape the dough logs.
Bake for 30-35 minutes. The vanilla portion of the dough should be slightly browned on top and more browned along the bottom edges. Remove from the oven and allow to cool for 10 minutes. Slice them diagonally, approximately ½ inch thick each. Allow to cool to room temperature. (Or, if you want to go the traditional route, lay each cookie down on the baking pan and bake an additional 10-15 minutes until the tops start browning.)