In a large mixing bowl, beat together the butter and sugars until combined, about 2-3 minutes. Add the Greek yogurt, Irish cream and vanilla extract, beating until smooth. Beat in the eggs one at a time.
Add the flour, baking powder, baking soda and salt and mix until just combined.
Mix together the flour, sugar and cinnamon in a medium bowl. Add the melted butter and Irish cream and mix until combined.
Preheat oven to 350°F. Grease an 8x8 baking pan. Pour half of the batter in, spreading to all four corners. Top with half of the streusel mixture. Pour remaining batter over top and add the remaining streusel mix. Bake for 40-50 minutes or until a toothpick inserted in the center comes out clean.
While cake is cooling, make the glaze. Whisk together the powdered sugar and Irish cream until combined. Drizzle over the cake after it has cooled for 15 minutes and serve.
Notes
All refrigerated items should be at room temperature, which helps the batter mix easily and evenly.
The batter is thick so use an offset spatula to spread evenly in the pan.
Allow the cake to completely cool before adding the glaze.
Use parchment paper in the pan if you want to take the entire cake out.