Preheat the oven to 350 F, position a rack in the middle of the oven. Grease a loaf pan with little butter and dust with flour to coat the pan, or you may use parchment paper.
Sift the cocoa powder into a bowl, add 2 tablespoons lukewarm water, mix to combine well. Set aside.
In a medium mixing bowl, sieve flour, baking powder, and baking soda. Add salt, whisk the dry ingredients until well combined. Set aside.
In the bowl of your stand mixer fitted with the paddle attachment, beat the butter and sugar on medium-high speed until light and creamy, scraping down in between, should take about 2-3 minutes. Or you can use an electric hand mixer/beater.
Add in the yogurt next, continue beating on medium-high speed.
In goes the vanilla extract next. Beat on medium speed for another 30 seconds
Now reduce to the lowest possible speed, alternately add the dry ingredients and milk, starting with flour and ending with flour. ( DO NOT OVER MIX ) .
Transfer 2 tablespoons of the cake batter into the bowl containing the chocolate batter, fold in gently.
Transfer half of the vanilla batter to the prepared baking tin, drop few spoonfuls of chocolate batter in random positions. Take a toothpick/skewer/butter knife and gently create swirls, do not over mix both the batters.
Top it with remaining vanilla batter, and add the remainder of the chocolate batter, creating random swirls once again. Give the loaf tin a gentle tap, bake on the middle rack for 40-45 min or until the toothpick inserted in the center of the cake comes out clean.
Cool the cake on a rack in the tin for 15 minutes, then remove from the tin and cool on the rack completely. Slice the cake only once it has cooled down completely.