Preheat oven to 350°.
Place eggs in a medium bowl; stir with a whisk until eggs are lightly beaten.
Combine milk, sugar, cocoa, and salt in a medium saucepan over medium heat. Cook until sugar dissolves, stirring occasionally (about 3 minutes). Add vanilla and chocolate; stir until chocolate melts.
Gradually add 1/4 cup hot milk mixture to eggs, stirring constantly with a whisk. Add egg mixture to milk mixture in pan, stirring with a whisk to combine. Pour into 8 (4-ounce) ramekins. Place ramekins in a 13 x 9-inch baking pan; add hot water to pan to a depth of 1 inch. Bake at 350° for 35 minutes or until a knife inserted in center comes out clean. Remove ramekins from pan; cool completely on a wire rack. Chill 8 hours or overnight.