Preheat oven to 325°.
Combine eggs, yolks and sour cream in a small bowl and mix to combine.
Add sugar, flour, baking powder and baking soda in the bowl of a stand mixer fitted with the paddle attachment. Combine ingredients. Note: a hand mixer may also be used.
Add softened butter and mix on low speed for 3 minutes.
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 and 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 at 325° 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.