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Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9×13-inch pan.
Make streusel topping: Combine sugar, flour, and cinnamon in a medium bowl. Cut in butter until mixture resembles coarse crumbs. Set aside.
Make cake: Combine flour, sugar, baking powder, and salt in a large bowl. Cut in butter until mixture resembles coarse crumbs. Whisk together egg and milk in a separate bowl, stir in vanilla.
Pour egg mixture into crumb mixture; mix just until moistened. Spread into the prepared pan and sprinkle with streusel topping.
Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, 25 to 30 minutes. Allow to cool before slicing