Preheat your oven to 350°F. Line a standard 12-cup muffin pan with paper liners and lightly spray the liners with nonstick spray.
In a large bowl, whisk together the sugar, eggs, milk, oil, vanilla, and vinegar.
Set a fine-mesh sieve over the bowl and add the flour, cocoa powder, baking powder, baking soda, espresso powder, and salt. Gently sift to combine.
Stir just until everything is combined and no dry spots remain, then fold in the chocolate chips. The batter will be quite thick. Don’t worry, that’s what you want.
Fill each muffin cup to the top (yes, all the way). This helps create that high rise. Sprinkle the tops with coarse sugar for a little crunch.
Bake for 20 to 25 minutes, checking doneness with a toothpick. It should come out clean or with just a few moist crumbs.
Let the muffins rest in the pan for 5 minutes, then move them to a wire rack to cool for another 10 to 15 minutes.
Make the filling (while the muffins bake):
In a small saucepan, combine the sugar, cream, cocoa powder, butter, and salt. Cook over medium low heat, stirring constantly, until the mixture is smooth, glossy, and just starting to bubble, about 1 to 2 minutes.
Remove from heat and let it cool slightly. Transfer to a piping bag or a zip-top bag (snip the corner when you're ready to fill). I like to place the bag in a tall glass to keep it upright while filling.
Fill the muffins:
Once the muffins are warm but not piping hot, use a paring knife to cut a tunnel into the center of each one, go almost to the bottom. If you want extra room for filling, you can pull out a small plug of muffin, but it’s not essential. The filling will still pipe in just fine without the extra step.
Snip a small hole in your piping bag and insert it into each slit, squeezing in the warm filling until it just starts to ooze out the top. Repeat for all the muffins. Best eaten warm when the centers are gooey.
Notes
Use Dutch-process cocoa for deeper chocolate flavor and the right chemical reaction with baking soda.Don’t skip the vinegar. It reacts with the baking soda to give the muffins their tall, tender rise.Mix gently to avoid tough muffins. Stir until just combined. A few lumps are fine.Fill muffin cups to the top for that bakery-style dome.Fill while muffins are still warm: A warm muffin lets the fudgy filling melt into the crumb, so you usually don’t need to hollow it out. If the muffins have cooled completely, carve out a small center to make room for the chocolate lava filling.Microwave to reheat for 15–20 seconds to bring back the gooey center.Want a sourdough version: Try my chocolate sourdough muffins.