Steamed Chocolate Pudding Cake

2 eggs
1 cup sugar
1 cup milk
2 tablespoons unsalted butter, melted
1/2 teaspoon pure vanilla extract
1 1/2 ounces unsweetened chocolate, melted
1 1/2 cups all purpose flour
1/4 teaspoon salt
1 1/2 teaspoons baking powder

Heat oven to 350 degrees. Thickly butter 8 ovenproof ramekins, coffee cups, or custard cups. Whip the eggs in a mixer fitted with a whisk attachment ( or using a hand mixer) until light and fluffy. Add the sugar and mix until combined. Add the milk, butter, vanilla, and chocolate and mix until combined. Sift the flour with the salt and baking powder twice. Add to the egg mixture and mix until combined. Pour the batter into the ramekins, filling each about 2/3 full. Cover each cup with foil. Arrange the cups in a hot-water bath and bake until firm on top, 30 to 40 minutes. Remove the cups from the water and remove the foil. Serve warm.