Heat the oven to 350°F (175°C). Grease a 9-inch square baking pan and line it with parchment paper, leaving enough overhang to lift out the cooled cake.

Combine the flour, sugar, and cinnamon for the crumb topping. Cut in the cold butter with a fork or pastry blender until coarse crumbs form, then refrigerate the topping while preparing the batter.

Beat the softened butter and granulated sugar for 2–3 minutes, until the mixture looks light and creamy. Scrape the sides of the bowl as needed so the butter blends evenly.

Beat in the egg and vanilla extract until incorporated. The mixture may look slightly uneven for a moment, but it will come together when the dry ingredients are added.

In a separate bowl, whisk together the flour, baking powder, and salt. This distributes the baking powder and salt throughout the flour before they reach the batter.

Add the dry ingredients to the butter mixture in portions, alternating with the milk. Mix only until combined; the batter will be fairly thick.

Gently fold in the blueberries with a spatula. Use a light touch to keep the berries intact and prevent the batter from becoming heavily streaked.

Spread the batter evenly in the prepared pan. Scatter the chilled crumb topping over the entire surface, breaking up any pieces that are unusually large.

Bake for 40–50 minutes, or until the top is golden and a toothpick inserted into the center comes out clean or with a few moist crumbs. Begin checking near the 40-minute mark, since ovens and berries can vary.

Cool the cake in the pan for at least 15–20 minutes before slicing. Use the parchment overhang to lift it onto a board if desired, then cut into about 9 servings.