Melt the chocolate in a microwave oven in 30-second bursts, stirring it between each until it's completely melted and smooth. (This can also be done in a bowl over a pan of boiling water.)
With a mixer, beat the eggs until they become very light and almost foamy.
Add 1/2 cup of the sugar to the eggs. Beat until the sugar is no longer gritty.
When the melted chocolate has cooled until just warm to the touch, pour it into the beaten egg, and stir it in with a rubber spatula. It's okay for there to be streaks. Add 1/3 cup of milk, vanilla extract, and red food coloring. Stir until the streaks are almost gone.
In a separate bowl, beat the remaining sugar and the butter into the flour until it has the texture of cornmeal. Add 1 cup of milk, and stir first with a kitchen fork then with a rubber spatula until all the flour is damp. (Add a little more milk if necessary.)
Spoon the flour mixture into the chocolate mixture. With a rubber spatula, stir until well blended.
Spoon the batter into a deep, buttered baking pan. Bake at 350 degrees for 35 minutes, or until a skewer inserted into the center comes out clean.