Preheat the oven to 400F. Grease 6 holes of a muffin pan with a light layer of coconut oil and cocoa powder, then flip it over and gently tap away the excess powder. Add the almond milk and vinegar to a large bowl and stir. Set aside for 5 minutes.
Melt the chocolate chips in a saucepan or double boiler over low heat, stirring often. Add the coconut oil, vanilla, sugar, and applesauce to the almond milk and beat with a whisk until the mixture gets frothy. It may be a bit lumpy, especially if the almond milk was cold.
Add the cocoa powder, flour, salt, and baking powder. Whisk until the large lumps are gone then stir in ⅓ cup melted chocolate chips, reserving the rest for toppings.
Spoon ¼ cup of batter into each of the 6 greased muffin holes. Gently place a square of chocolate (2 if you're feeling fancy!) into the batter and push down slightly. Evenly divide the remaining batter to cover the chocolate pieces.
Bake at 400F for 13-17 minutes. You want the outside to be fully cooked and the inside to be gooey and melty. Keep a close eye on the lava cakes after 13 minutes and pull them out when the top of the cakes has a a bit of a sheen but doesn't look completely wet.
Let the pan sit for 1-2 minutes, then place a cookie sheet on top of the pan and flip it over to release the lava cakes. Top the cakes with the remaining melted chocolate chips and a light dusting of cocoa powder or powdered sugar.
Serve immediately or let cool completely before transferring to the fridge.