1/2 cup (1 stick) unsalted butter, room temperature, plus more for pan
2 1/2 cups all-purpose flour, plus more for pan
2 tablespoons instant espresso powder
1 teaspoon baking powder
1 teaspoon baking soda
1 teaspoon ground cinnamon
1 teaspoon kosher salt
1/4 teaspoon ground cardamom
3/4 cup strong brewed coffee, room temperature
1/2 cup sour cream
1 teaspoon vanilla extract
1 1/4 cups granulated sugar
3 large eggs plus 1 egg yolk, room temperature
1 cup powdered sugar
2 tablespoons coffee liqueur
1 tablespoon sour cream
A 10-inch tube pan
Directions
Using your fingers, combine flour, butter, brown sugar, powdered sugar, espresso powder, and salt in a medium bowl until mixture sticks together when pressed. Chill until ready to use.
Melt chocolate and butter in a heatproof bowl set over a pot of simmering water (water should not touch bowl) or in the top of a double boiler over medium heat. Remove from heat and stir in pecans, coffee, and granulated sugar.
Preheat oven to 350°F. Butter and flour tube pan, tapping out excess flour. Whisk 2 1/2 cups flour, espresso powder, baking powder, baking soda, cinnamon, salt, and cardamom in a medium bowl. Whisk coffee, sour cream, and vanilla in another medium bowl.
Beat granulated sugar and 1/2 cup butter in a stand mixer fitted with the paddle attachment until light and fluffy, about 3 minutes. Beat in eggs and egg yolk one at a time, mixing well after each addition. Add dry ingredients in 3 additions, alternating with coffee mixture in 2 additions, scraping down sides of bowl after each addition.
Scrape one-third of the batter into prepared pan; smooth the surface. Drizzle half of the chocolate swirl mixture over. Add another one-third of the batter; smooth the surface. Drizzle the remaining chocolate swirl mixture over, then scrape in the remaining batter; smooth the surface. Sprinkle crumb topping over. Bake cake until a tester inserted into the center comes out clean and cake springs back when pressed, 40–50 minutes. Let cool completely in pan on a wire rack.
Run a butter knife around the perimeter of pan to loosen cake. Gently invert cake onto a large plate, then return cake (crumb side up) to rack.
When cake is cool, prepare the glaze. Whisk powdered sugar, coffee liqueur, and sour cream in a medium bowl. Using a spoon, drizzle glaze over cooled cake, holding the spoon a few inches above the cake.
Cake can be made up to two days before serving. Store wrapped in plastic until ready to serve.
