1. For the gooey center: Combine the milk chocolate, heavy cream and butter in a small saucepan and heat over low heat, whisking until the chocolate is completely melted and smooth. Pour this mixture into a small glass baking dish and chill until set, about 1 hour. Scoop and roll into 12 small balls and place on a small parchment-lined plate or tray. Wrap and chill for at least 30 minutes up to overnight.
2. For the muffins: Preheat the oven to 375 degrees F. Line a 12-cup muffin tin with your favorite liners.
3. Fill a medium saucepan with about 1 inch of water and bring to a simmer. Combine the butter and bittersweet chocolate in a heat-safe bowl that fits comfortably in the saucepan without touching the water. Stir occasionally until the chocolate is completely melted and smooth, 3 to 4 minutes. Remove from the heat.
4. Combine the flour, sugar, cocoa, baking powder, salt and baking soda in a large bowl.
5. Whisk the milk, vanilla and egg together in a separate medium bowl. Stir the melted chocolate into the milk mixture.
6. Pour the chocolate mixture into the dry ingredients and fold until just combined (don't worry if there are lumps, this means your batter isn't over-mixed).
7. Fill each liner with about 1 heaping tablespoon of batter and spread to cover the bottom. Place a chocolate ball in each cup and evenly top each with the remaining batter. Smooth the top with a small, greased offset spatula. Lightly tap the muffin tray on the counter to make sure the batter settles.
8. Bake, rotating halfway through, until the top is nicely cracked and springs back when touched, 14 to 16 minutes. Let rest 3 minutes in the pan, then serve warm with a big glass of milk!
An alternate way to melt the chocolate mixture is to microwave in 30-second intervals, stirring until smooth.