Heat oven to 325 F. Grease and line an 8 x 8 inch square cake pan with parchment paper. In a small bowl, toss the apples with the lemon juice, cinnamon, and sugar.
Make the crumbs: In a small saucepan over medium heat, brown the butter. Stir in the brown sugar, granulated sugar, cinnamon, salt, and all-purpose flour into the melted butter. The mixture should hold together in clumps. Set the streusel aside.
Beat butter with the sugar in the bowl of a stand mixer using the paddle attachment, at medium-high speed, until light and fluffy.
Add in the egg, sour cream, and vanilla extract. Beat until combined.
Sift the flour, baking powder, and salt, into the wet ingredients. Then beat until just combined.
Pour the cake batter into the prepared pan and smooth the top using a rubber spatula.
Dump the apples on top of the batter and arrange to form a relatively even layer. There's no need to make them pretty, since they're about to get topped with streusel.
Dump the streusel on top of the apples in handfuls, squeezing bits of of streusel together to form large-ish clumps.
Bake 50-55 minutes until a toothpick inserted into the center of the cake comes out dry.
Cool 5 minutes in pan, then remove (using the parchment paper as a sling) to a wire rack to fully cool.