Preheat oven to 425°F (220°C). Grease a jumbo (6-count) or standard (12-count) muffin tin generously.
In a large bowl, cream the butter, granulated sugar, and brown sugar until light and fluffy, about 2–3 minutes.
Slowly mix in the oil. Add sour cream, milk, vanilla, and eggs, mixing until smooth and fully combined.
Sprinkle flour, baking powder, baking soda, and salt over the batter. Mix just until combined. Do not overmix.
Gently fold in mini chocolate chips and chocolate chunks.
Remove ⅓ of the batter to a separate bowl. Stir in cocoa powder, sugar, espresso powder (if using), and milk until smooth.
Spoon plain batter into muffin wells, filling about ⅔ full. Add small spoonfuls of chocolate batter, then top with more plain batter. Gently swirl with a toothpick or skewer. Sprinkle tops with mini chocolate chips.
Bake at 425°F for 8–10 minutes, then reduce oven temperature to 350°F (175°C) without opening the door.
Continue baking-- Jumbo muffins: 15–20 minutes, Standard muffins: 10–12 minutes (Muffins are done when a toothpick inserted comes out with a few moist crumbs.)
Let muffins cool in the pan for 5 minutes, then transfer to a wire rack.