Preheat your oven to 425°F.
Generously butter the inside of your ramekins, then lightly coat them with cocoa powder. Tap out any excess. This helps the cakes release easily without leaving a white flour coating on the chocolate.
In a microwave-safe bowl, combine the chocolate chips and butter. Microwave in 30-second increments, stirring well after each one, until completely melted and smooth. Set aside to cool slightly.
In a separate bowl, combine the whole eggs, egg yolks, and sugar. Beat for about 2 minutes, until the mixture is smooth and slightly lighter in color.
Add the flour, followed by the melted chocolate and butter mixture. Gently mix until everything is completely incorporated and you have a smooth chocolate batter.
Divide the batter evenly among the prepared ramekins. Place them in the preheated oven and bake for approximately 12–13 minutes. The edges should look set, but the centers should still be soft.
Remove from the oven and allow the cakes to rest for 1–2 minutes. Carefully run a thin knife around the edges if necessary, place a plate over each ramekin, and flip to release the cake.
Dust with powdered sugar and serve immediately. I love adding a generous scoop of vanilla ice cream right on top so it begins melting into that warm chocolate center.