In a medium-large bowl, combine the yogurt, sugar, eggs and the vanilla extracts. Whisk until well blended.
Add the baking powder and salt. Whisk to combine then add the flour and whisk again just until all of the flour is blended in.
Add the oil and stir well. Don't worry, at first it will seem to separate but keep stirring till smooth.
Remove ½ cup of the batter to a medium-size bowl (the bowl should be at least one cup) or a 1 cup measuring cup with a spout (works best). Add 2 tablespoons of brown sugar (light or dark), 2 teaspoons cinnamon and 1 tablespoon milk to this batter. Stir until nice and smooth.
Pour approximately (doesn’t have to be exact) ¼ of the plain mixture into the prepared pan, pouring into the center of the pan and allowing the batter to spread. The mixture will spread out and cover about ¾ of the bottom of the pan. Now pour approximately ¼ of the cinnamon batter on top of the plain batter in the pan. Again, pour right in the center of the pan.
Continue this pattern, each time pouring into the center of the pan, until both batters are used up. Because there is much more of the plain batter, each pour will be more than the cinnamon batter pours. There is a pictorial tutorial of this above in the post to make these directions more easy to understand.
Place the cake in the preheated oven and bake for 30-40 minutes, until the cake feels springy to the touch and a toothpick or cake tester inserted into the center comes out clean or the center of the cake registers 200-205˚F on an instant thermometer (best way to tell when a cake is done). Be careful not to overbake.
Remove the cake from the oven and allow to cool in the pan for 8 minutes, then flip it out onto a cooling rack (the bottom of the cake will become the top). While the cake is cooling in the pan, prepare the glaze.