In a saucepan, melt the butter over medium heat, stirring often until it turns golden brown and smells nutty.
Remove from heat and let it cool slightly.
In a large mixing bowl, whisk together the browned butter and sugar until combined.
Add eggs one at a time, whisking well after each addition.
Stir in vanilla extract and cream cheese, mixing until smooth.
Sift in flour, baking soda, and baking powder. Fold gently until no dry streaks remain.
Divide the batter into two equal portions.
In one half, add the cocoa powder and dissolved coffee mixture; mix until smooth.
In the other half, add the cinnamon powder and mix well.
Lightly grease and line an 8.5-inch loaf pan with parchment paper.
Alternate spoonfuls of the coffee-cocoa batter and cinnamon batter into the pan.
Use a knife or skewer to swirl gently for a marbled effect.
Bake in a preheated oven at 180°C (350°F) for 40–45 minutes, or until a skewer inserted in the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.