Prepare a square 8x8 baking pan with parchment paper and preheat the oven to 350 F/180 C.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt and set it aside.
In another small bowl, mix together the dark brown sugar and cinnamon and set it aside.
In a stand mixing bowl, cream together the butter and sugar until light and fluffy, about 3 minutes.
Whisk together the eggs and vanilla extract and slowly stream them into the mixing bowl, mixing well until fully combined.
Mix in half of the dry ingredients on low speed until almost combined, then add the greek yogurt. When the yogurt is almost combined, add the rest of the dry ingredients and mix until just combined.
Evenly spread half of the batter into the prepared baking pan.
Sprinkle all but 2-3 tablespoons of the cinnamon sugar mixture over the batter, then spread the rest of the cake batter on top.
Sprinkle the rest of the cinnamon-sugar over the top then bake the cake for 30-33 minutes, or until the middle is puffy and it bounces back when touched.
Let the cake cool completely on a wire cooling rack. Meanwhile, whisk together the powdered sugar, milk, and vanilla until smooth. When the cake is cool, drizzle the glaze over the top and enjoy!