A springform pan is best because you can remove the sides and slide the cake out without disturbing the crumbs on top. If you have only a plain cake pan, though, that will work too; just make sure it’s at least 3 inches tall on the sides so the crumbs and batter don’t spill while baking.
Brown Butter-Cinnamon Crumb Cake
2 hours, largely unattended
1. Make the crumb topping: Put the butter in a medium skillet and place over medium-high heat. Once the butter melts, continue cooking, whisking occasionally, until the butter foams and then starts to smell nutty, 3 to 5 minutes. As soon as you see light brown flecks on the bottom of the skillet (these are the milk solids caramelizing), remove the pan from the heat and use a heatproof rubber spatula to scrape the butter and all the browned bits on the bottom of the pan into a medium bowl. Whisk in the cinnamon until smooth, then place the bowl in the freezer for 10 minutes, stirring two or three times while it chills, to cool the butter until no longer warm.
2. Remove the butter from the refrigerator and add the flour, followed by both sugars and the salt. Using your hands, mix and knead the mixture until it forms a clumpy dough. Transfer the bowl to the freezer and keep the crumble topping cold while you prep the cake batter.
3. Heat the oven to 325 degrees. Grease a 9-inch round springform pan with some butter and line the bottom with a round of parchment paper. Grease the paper, then coat the inside with flour, tapping out the excess. Place the pan on a parchment paper-lined baking sheet.
4. Make the cake batter: In a medium bowl, whisk together the flour, baking powder, salt and baking soda. In a large bowl, combine the butter, sugar and vanilla and beat with a wooden spoon or a hand mixer until creamy and fluffy, about 1 minute. Add one egg, beat until it absorbs into the batter, then add the second egg and beat until smooth. Beat in the sour cream.
5. Add one-third of the dry ingredients followed by half the milk to the batter, then stir with a whisk until almost combined. Add half the remaining dry ingredients followed by the remaining milk, then stir again until almost combined. Add the remaining dry ingredients, then stir with a rubber spatula until the batter just comes together and there are no patches of flour visible.
6. Scrape the batter into the prepared baking pan and smooth the top. Using your fingers, break up the chilled topping into crumbles — some the size of whole walnuts and some the size of peas — as you sprinkle it evenly over the batter. Try not to pile all the crumbs in the center but evenly cover the surface so the batter doesn’t get squeezed out.
7. Place the pan in the oven and bake until golden brown on top and a toothpick inserted in the center of the cake comes out clean, about 1 hour and 20 to 30 minutes. Transfer the cake to a wire rack and let cool completely before unmolding. Dust the top with powdered sugar, if you like, and cut into wedges to serve.
The cinnamon-brown butter will keep in an airtight container in the refrigerator for up to 1 week. Soften to room temperature again before using. The baked cake will keep in an airtight container at room temperature for up to 1 week.