Preheat oven to 350°F and position rack in the center
Butter a 13x9-inch baking pan
Make the coffee ribbon by mixing 3 tablespoons packed light brown sugar, 2 teaspoons ground cinnamon, and 1 tablespoon instant coffee granules
Make the crumb topping by mixing 1 ¼ cups all-purpose flour, ½ cup packed light brown sugar, 2 teaspoons instant coffee granules, ¾ teaspoon ground cardamom, and ¼ teaspoon kosher salt
Work 1 stick of room temperature unsalted butter into the crumb topping mixture until it resembles coarse crumbs with no floury spots
In a bowl, combine 3 ½ cups all-purpose flour, 2 ½ teaspoons baking powder, 1 ½ teaspoons kosher salt, and ½ teaspoon baking soda
In another bowl, mix ½ cup brewed coffee, 1 tablespoon instant coffee granules, 2 teaspoons vanilla extract, and ⅔ cup sour cream
In a stand mixer, cream together 12 tablespoons room temperature unsalted butter, 1 cup granulated sugar, ¾ cup packed light brown sugar, and ¼ cup neutral oil until pale and fluffy
Add 4 large eggs one at a time to the butter mixture, mixing well after each addition
Alternately add the dry ingredients and wet ingredients to the butter mixture, starting and ending with dry ingredients
Fold the batter by hand with a spatula until evenly mixed with no floury spots
Spread half of the batter into the prepared pan
Sprinkle the coffee ribbon mixture evenly over the first layer of batter
Spread the remaining batter over the ribbon layer
Scatter the crumb topping over the batter
Bake at 350°F for approximately 40 minutes until a cake tester comes out clean
Allow the cake to cool before serving
