Preheat your oven to 375°F (190°C). Grease and flour an 8x8 inch baking pan.

Prepare the streusel: In a medium bowl, combine the flour, sugar, and cinnamon for the topping. Cut in the cold butter using your fingers or a pastry blender until the mixture resembles coarse crumbs. Set aside in the refrigerator.

Prepare the cake batter: In a large bowl, cream together the softened butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla extract.

In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, alternating with the milk, mixing just until combined. Do not overmix.

Spread the batter evenly into the prepared baking pan. Arrange the apricot halves/quarters evenly over the top of the batter.

Sprinkle the reserved streusel topping generously over the apricots and batter mixture.

Bake for 35 to 40 minutes, or until a wooden skewer inserted near the center comes out clean. Let cool slightly before serving warm, perhaps with a dollop of whipped cream.