1⁄2 cup firmly packed light brown sugar
1⁄2 teaspoon ground cinnamon
Pinch of salt
6 tablespoons cold unsalted butter, cut into 1⁄2-inch cubes
3⁄4 cup all-purpose flour

To make the crumb topping, in a bowl, stir together the brown sugar, cinnamon, and salt. Using your fingertips or a pastry cutter, add the butter and the flour and mix well until pea-sized clumps form. Set aside.

Nonstick cooking spray
11⁄2 cups all-purpose flour
3⁄4 teaspoon baking powder
1⁄4 teaspoon baking soda
1⁄4 teaspoon salt
1⁄3 cup buttermilk
1⁄3 cup whole milk
6 tablespoons unsalted butter, at room temperature
1⁄2 cup granulated sugar
1 large egg
2 teaspoons vanilla extract

To make the doughnuts, preheat the oven to 375°F. Coat the wells of a doughnut pan with nonstick cooking spray. In a bowl, whisk together the flour, baking powder, baking soda, and salt. In a measuring cup, stir together the buttermilk and whole milk. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment, beat together the butter and granulated sugar on medium speed until light and fluffy, about 2 minutes. Scrape down the sides of the bowl. Add the egg and vanilla and beat on medium speed until combined, about 1 minute. On low speed, add the flour mixture in 3 additions, alternating with the milk mixture and beginning and ending with the flour. Beat each addition until just blended.

Pour 2 tablespoons batter into each prepared well. Sprinkle each with about 2 tablespoons topping. Bake, rotating the pan 180 degrees halfway through baking, until a toothpick inserted into the doughnuts comes out clean, about 10 minutes. Let cool in the pan on a cooling rack for 5 minutes, then invert the doughnuts onto the rack and let cool completely.

Meanwhile, wash and dry the pan and repeat to bake the remaining batter.