Preheat the oven to 350F and grease and line a 9x5 inch loaf pan with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In another bowl, whisk the 3/4 cup milk, yogurt, oil, and vanilla, then fold into the dry ingredients just until smooth.
Transfer 1/3 of the batter to a small bowl and stir in the cocoa powder and remaining 3 tbsp milk until smooth.
Drop alternating spoonfuls of vanilla and chocolate batter into the pan, then drag a skewer through in 3-4 figure-eight motions. Do not overswirl or the marble pattern will blur.
Bake for 50-55 minutes, until a toothpick comes out clean. Tent with foil after 35 minutes if the top is browning too quickly.
Cool in the pan for 15 minutes, then lift out and cool completely on a rack before slicing to reveal the swirls.
