Preheat the oven to 400 degrees and place the chocolate pieces in a medium to large sized bowl.
Add milk and cornstarch in a saucepan and whisk over medium heat until brought to a simmer. Cook, stirring constantly, until thick, about 1 minute. Pour over chocolate pieces and stir until chocolate is fully melted.
Combine the egg yolks, whipping cream and vanilla extract in a bowl and whisk. Slowly mix the egg yolk mixture into the chocolate mixture and set aside.
Using a hand or a stand mixer, beat the egg whites in a separate bowl until they become frothy. Add the cream of tartar. Add the sugar, a little at a time while beating, until stiff glossy peaks form. This should take about 5-7 minutes.
Gently fold in the egg whites, being sure not to over mix. The batter should be light and fluffy and still full of the air bubbles from the egg whites.
Fill each ramekin halfway full with the batter. Add a piece of the milk chocolate in the center of each (this step is optional but I love it). Top them off with the remaining batter.
Place the ramekins on a baking sheet on the bottom rack and bake for 10-12 minutes, or until the souffle rises and a toothpick comes out clean. Rotate the baking sheet halfway through to account for any uneven oven temperatures.
Dust with a little powdered sugar and serve immediately.