Preheat oven to 180°C (350°F) Gas mark 4, with the rack in the middle.
Line the bottom and sides of a 9-inch square baking tin with heavy-duty foil, leaving an overhang on 2 sides.
Butter the bottom and sides of the tin, then dust with flour, knocking out any excess flour.
Stir together the plain flour, sugars, cinnamon, and a pinch of salt in a large bowl.
Blend in the butter with your fingertips or a pastry blender until mixture forms large clumps.
Whisk together the flour, baking powder, baking soda, and salt in a bowl.
Stir together sour cream and vanilla in a small bowl.
Beat together the butter and sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 5 minutes. Add the egg and beat until well blended.
At low speed, mix in the flour mixture in 3 batches, alternating with sour-cream mixture and mixing until just combined.
Gently fold in the blueberries.
Spoon the batter into the tin, smoothing top.
Crumble half of the topping evenly over batter.
Bake for 20 minutes, then remove from oven and crumble remaining topping evenly over cake.
Bake for a further 20 minutes.
Allow the cake to cool in the tin for about 10 minutes.
Lift out the cake using foil and let it cool down completely on rack.
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