Preheat the oven to 375 degrees. To make the topping, in a medium bowl, combine brown sugar, flour, salt, and cinnamon. Add butter, and work in, using your fingers or a pastry cutter, until well combined; set aside
To make the batter, in a medium bowl, whisk together flour, baking powder, baking soda, and salt; set aside. In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and sugar until light and fluffy. Add the egg and vanilla, and beat to combine. Add the dry ingredients, alternating with the sour cream and buttermilk, and beginning and ending with the dry ingredients; scrape down the bowl as necessary.
Spray eighteen cups of a mini-muffin tin with nonstick cooking spray. Divide batter evenly between cups. Sprinkle topping over batter. Bake until a cake tester inserted in the center comes out clean, about 15 minutes. Let stand in pans for 5 minutes. Remove to wire racks to cool. Use immediately.