Preheat the oven to 375°F and set an oven rack in the middle position. Grease an 8-inch square pan with butter or nonstick cooking spray.
In a medium bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and salt. Set aside.
In the bowl of an electric mixer, beat the butter/margarine and granulated sugar until creamy, about 2 minutes.
Add the eggs one at a time, scraping down the sides of the bowl and beating well after each addition. Beat in the vanilla extract and lemon zest.
Gradually add the flour mixture, alternating with the milk, beating on low speed to combine.
Fold in the berries until evenly distributed. Do not over-mix.
Transfer the batter to the prepared pan and spread evenly. Sprinkle the streusel topping evenly over the batter.
Bake for 50 to 55 minutes, until golden brown around the edges and a cake tester comes out clean.