Prepare a 9" or 10" Bundt pan by generously spraying the inside with non-stick baking spray or melted butter. Lightly dust with flour.
Preheat oven to 325℉ (163℃)
Filling
Combine brown sugar, espresso powder and chocolate chips in a bowl. Set aside.
Cake Batter
Mix eggs, yolks and sour cream together in a bowl. Set aside.
Place sugar, flour, baking powder and baking soda in the bowl of a stand mixer fitted with the paddle attachment. Mix on medium-low speed until ingredients are combined. Note: a hand mixer may also be used.
Add softened butter to mixing bowl. Mix on low speed for 3 minutes. Mixture will appear crumbly.
Add half of the egg/sour cream mixture to the mixing bowl and combine on low speed for one minute. Scrap sides of bowl.
Add remaining egg/sour cream mixture to the mixing bowl. Combine on low speed for one minute. Scrape sides of bowl and mix on low speed for another minute.
Add ½ of the cake batter to the prepared pan and smooth with a rubber spatula.
Scatter the chocolate/espresso/brown sugar mixture on top of the batter in the Bundt pan. Add the remaining batter and smooth with a rubber spatula.
Bake for 50 minutes or until top is quite brown and a toothpick inserted in the center comes out clean.
Remove pan from oven and cool upright for 10 minutes.
Flip pan upside down onto a cooling rack and let cool completely. Remove pan - cake should release from pan on its own. If not, use blunt knife and gently loosen sides.
Coffee Drizzle
Mix powdered sugar and espresso together until smooth. Use a pastry bag or spoon to drizzle over cake.