Preheat oven to 350 degrees.
Butter an 8" pie plate and set aside. (I always use the butter wrapper to grease my dish - it usually has just enough to get the job done)
In a microwave safe bowl, melt the chocolate and butter in 20-30 second increments, stirring between intervals, until combined. Let it cool.
In another bowl, mix the sugar into the beaten eggs until fully incorporated.
Add the cooled butter/chocolate mixture into the sugar mixture and stir until completely combined.
Add the vanilla and milk and stir well.
Fold in the flour, gently mixing just until no white steaks remain. Do not over mix.
Pour into the prepared pie dish and bake for 25 minutes.
Top with some ice cream while it's still warm.