Preheat oven to 350°F. Grease a 9x13 baking dish or line with parchment.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
In a large bowl, cream butter, granulated sugar, and brown sugar until light and fluffy (about 2-3 minutes).
Add eggs one at a time. Mix in vanilla and Greek yogurt.
Add dry ingredients alternately with milk. Mix just until combined- do not overmix.
Spread half of the batter into the prepared pan. Sprinkle half of the streusel over the batter. Add remaining batter (gently spread). Top with remaining streusel. *see note
Bake 35-40 minutes, or until a toothpick inserted in the center comes out clean.
Cool 15-20 minutes before slicing.
Whisk powdered sugar, milk, and vanilla until smooth. Drizzle over warm cake.