Make the filling by combining the sugar, cocoa and chocolate chips in a small bowl. Set aside.
Make the crumb topping by sifting the flour, cocoa, icing sugar and salt in a larger bowl. Stir in the sugar and vanilla. Then add the cold cubed butter and rub it into the dry ingredients with your fingers until no dry flour is left and you have a range of large and smaller pea-sized crumbs. Add the chocolate chips and then refrigerate till you need it. I found that keeping this topping mixture cold leads to crunchier crumbs compared to the room temperature butter recommended in the original recipe linked below.
Make the cake by first stirring together the milk and lemon juice and setting it aside while you make the batter.
Now preheat the oven to 175 C. Line an 8 inch square pan with non-stick baking paper leaving a little overhang for easy removal. Set aside.
For the batter, use either a stand mixer with a paddle attachment (recommended because the batter can get a little messy) or a large mixing bowl and hand mixer.
In the bowl, sift together the flour, cocoa, baking powder, baking soda and salt. Stir in the sugar.
Add the cubed butter and beat for a minute or two until the mixture looks sandy and all the flour is moistened. Now add the vanilla and eggs and beat to combine into a thick, cookie-dough like batter. See photos below.
Add a splash of the soured milk to loosen the mixture and beat for a few seconds. Then add the rest of it slowly with the mixer running on low speed. Beat until smooth. If many lumps remain, whisk the batter by hand to smoothen further, but be gentle and do not over mix it. Finally, stir in the chocolate chips.
To assemble the cake, add half the batter to the prepared pan. Smoothen it out then scatter all of the filling in an even layer over the batter. Top with the remaining batter and smoothen it out again. Finally, scatter the crumb topping all over, then gently press it down with the back of a spoon to help it stick and make it easier to slice the cake later.
Bake for 40 minutes, then an additional 5 to 10 minutes until a toothpick comes out with moist crumbs and no wet batter. You may get some melted chocolate, that's ok!
Let the cake to cool in the pan for 30 minutes, then lift it out of the pan using the overhang and set on a wire rack to cool completely. Cut into 16 squares. I found that on day one, the cake was very soft and crumbled a little (not the crumb topping, the cake itself) so I do recommend waiting and cutting it on day two when it's firmer and actually tastes better.
Store in an airtight tin at room temperature for 4 to 5 days, in the fridge for about 10 days and in the freezer for longer. If the cake is cold, it's best eaten slightly warmed up as butter cakes harden in the fridge. The crumb topping will soften by day two but there is still a crunch from the sugar. I actually think this cake is great even without the crumb topping but that's personal preference :) Happy baking!