Preheat oven to 350F (175C) and line a 12-count muffin tin with paper liners. Set aside.
In a large bowl, whisk together oil, sugar, buttermilk, egg, vanilla extract, and sour cream until well-combined.
In a separate bowl, whisk together flour, cocoa powder, baking soda, instant coffee (if using), and salt.
Add the flour mixture to the wet ingredients and use a spoon or spatula to fold together until just barely combined.
Add chocolate chips and gently stir until they are incorporated into the batter and batter is combined, but do not over-mix (which can make the muffins dense and dry).
Set batter aside and prepare cheesecake filling.
In a large, clean bowl, stir together cream cheese and sugar until smooth and creamy (an electric mixer makes easy work of this and makes it easier to ensure your cream cheese is smooth and lump-free, but if the cream cheese is soft enough this can be done by hand).
Add sour cream and vanilla extract and stir until well-combined, then finally stir in the egg until incorporated. The batter should be smooth.
Scoop chocolate batter into prepared muffin tin, filling each paper liners halfway full. You will have some batter left, reserve this to use after you’ve added the cheesecake layer.
For a rich, thick pocket of cheesecake filling, take a spoon and use it to make a crater/divot in the center of each muffin.
Scoop a heaping tablespoon of cheesecake filling into the center of each muffin in the crater you just created (it won’t all fit, some will sit on top of the chocolate batter and this is fine).
Portion a small amount of remaining chocolate batter over the top of the cheesecake layer and use a toothpick to swirl the batters together. If desired, sprinkle tops with additional chocolate chips.
Transfer to 350F (175C) oven ad bake for 22-25 minutes or until muffins are baked through. A toothpick inserted in the center should come out mostly clean or with a few wet crumbs, but not wet batter (if the toothpick is very chocolatey, test again, you may have hit a melted chocolate chip!).
Allow muffins to cool in tin for 10-15 minutes before removing. While they may be puffed and rounded immediately after coming out of the oven, they'll sink in on themselves as they cool, this is normal and just due to the heavy cheesecake filling. Taste over beauty! These muffins may be enjoyed still warm or they may be allowed to cool completely and be refrigerated before enjoying!