Preheat oven to 350°F (177°C). Line an 8-inch square pan (9-inch square is too big, see Notes for other pan sizes) with lightly greased parchment paper or directly grease the pan. I usually use this square pan or this square pan.
Combine the brown sugar, flour, and cinnamon together in a medium bowl. Cut in the chilled butter with a pastry cutter or two forks (or use a food processor or your hands) until the mixture is in pea-sized crumbs. Some larger crumbs are OK. You’ll have a little over 2 cups of crumb. Refrigerate until step 5.
Whisk the flour, baking powder, baking soda, and salt together in a large bowl. Set aside. In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the butter and sugar together on high speed until smooth and creamy, about 3 minutes. Scrape down the sides and up the bottom of the bowl with a silicone spatula as needed. (Here’s a helpful tutorial if you need guidance on how to cream butter and sugar.) Add the eggs and vanilla, and beat on medium-high speed until combined. Beat in the sour cream. Scrape down the sides and up the bottom of the bowl with a silicone spatula and beat again as needed to combine. Mixture will be lumpy. Add the flour mixture to the wet ingredients, and beat on low speed until just combined. Finally, beat in the milk. Do not overmix this batter. The batter will be thick. You’ll have about 2 and 1/2 cups of batter.
Carefully spread about half of the batter into the prepared pan. Sprinkle 1 cup (about half) of the crumb mixture evenly on top. Carefully spread the remaining batter on top (every last drop of it!). This can be a little tricky since you’re spreading thick batter on top of crumbs, but do your best. I usually use a spoon or small offset spatula. It doesn’t have to be perfect. Sprinkle the remaining crumb mixture evenly on top. Bake for around 35–40 minutes or until the cake is baked through. To test for doneness, insert a toothpick into the center of the cake. If it comes out clean, it is done. Allow cake to cool in the pan set on a wire rack for 15 minutes.
Whisk all of the icing ingredients together. Drizzle over warm cake.
Lift the cake from the pan using the overhang parchment paper around the sides and slice into squares. Or, if you didn’t use parchment, slice directly in the pan. Serve cake warm or at room temperature.
Cover leftovers tightly and store at room temperature for up to 3 days or in the refrigerator for up 1 week.
