Preheat the oven to 350 degrees F (176 degrees C).
In a large mixing bowl using the paddle attachment, beat together the butter and sugar on medium speed for 2 minutes. Add eggs one at a time mixing 10-15 seconds between each addition.
Add the yogurt, vanilla and milk to the butter, sugar and eggs and mix on medium low for 1 minute to combine.
Sift the dry ingredients directly over the wet ingredients. Mix on medium low for 1 minute to combine all ingredients. The batter will be thick.
Divide the batter equally between 3 9-inch greased and lined cake pans.
Bake on the middle rack at 350 for 30-35 minutes, until a toothpick inserted in the center comes at clean. Remove to cooling racks and allow to cool in the pans for 15 minutes. Then turn them out onto the racks to finish cooling.
While the cakes are cooling, in a large mixing bowl using the whisk attachment, add the softened cream cheese and softened butter. Beat on medium-high speed for 7 minutes, scraping the sides every few minutes. Add the vanilla extract and beat for 30 seconds more.
Sift the powdered salt, sugar, and cocoa powder directly over the cream cheese and butter. Mix on low for 2 minutes until fully incorporated. Refrigerate 30 minutes up to 24 hours before frosting the cake. Mix on high 2 minutes right before frosting.
To frost the cake, use 1/4 of the frosting between the first and second layer, 1/4 between the second and third layers, and the remaining half for the top and sides.
Store in the refrigerator up to 5 days.