Preheat your oven to 350°F and grease or line a 9x9 inch square pan.
In an electric mixer, cream the butter and sugar together on high speed for about 3 minutes until it is light and fluffy. Scrape down the sides of the bowl. Then, add the two eggs and vanilla and continue beating for another minute until the mixture is very smooth and creamy.
In a small cup or bowl, whisk the milk and yogurt together until combined. Heat them for 10-15 seconds in the microwave to bring them to room temperature.
In a separate bowl, whisk together the flour, baking powder and salt.
With your mixer running on low, alternate adding half of the flour mixture, all of the milk mixture, and then the remaining flour mixture until a thick batter comes together. Make sure to not over-mix and stop as soon as the flour is just combined.
Toss the blackberries with the additional 1½ tsp of flour. Then, use a flexible spatula to fold them in to the batter. Transfer the batter to your prepared pan.
To make the crumb topping, mix all of the ingredients together until you get a soft dough, then crumble it in an even layer on top of your batter.
Bake for 35-45 minutes, or until a toothpick comes out clean. Let the cake cool.
To make the icing, whisk all of the ingredients together. Drizzle it over the cake once it has cooled down. Enjoy!