Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan or line a 9-inch square pan with parchment, leaving overhang for lifting.
Make the crumb topping by stirring flour, brown sugar, granulated sugar, cinnamon, and salt in a bowl. Pour in melted butter and mix until large clumps form. Refrigerate while you prepare the cake.
For the cream cheese layer, beat the cream cheese and sugar until smooth and fluffy. Mix in the egg, vanilla, and lemon zest until just combined. Set aside.
For the cake batter, whisk the flour, baking powder, baking soda, and salt in a bowl. In a separate bowl, cream the butter and sugar until pale and fluffy. Beat in the eggs one at a time, then the vanilla. Mix in the sour cream. Add the dry ingredients in two additions, alternating with the milk, and mix just until combined.
Fold the floured blueberries gently into the batter.
Spread the cake batter evenly into the prepared pan. Spoon the cream cheese mixture over the batter and gently spread into an even layer. Sprinkle the chilled crumbs evenly over the top, squeezing some into larger clumps.
Bake until the crumbs are golden and a toothpick inserted near the center (avoiding the cream cheese pockets) comes out with a few moist crumbs, 50–60 minutes.
Cool completely in the pan on a rack. Run a knife around the edges, release if using a springform, then slice and serve.
Store covered in the refrigerator for up to 5 days. Bring to room temperature before serving, or warm slices briefly if you like.