Chocolate Chip Cookie Cakes

Wet ingredients:

1/4 cup milk
2 teaspoons vanilla extract
Dry ingredients:
2 cups flour
1 teaspoon baking powder
1/2 teaspoon salt
4 ounces chocolate chips, plus extra for garnish
Creaming ingredients

1 stick butter
1 1/4 cups granulated sugar
3/4 cup brown sugar, packed
1 whole egg
1 egg yolk
For the icing:

1 cup heavy cream
1/4 cup superfine granulated sugar
1 stick soft unsalted butter
10 ounces bittersweet chocolate
2 teaspoons vanilla extract
Procedure

Preheat oven to 335 F. Place the rack in the middle position. Line 14 cupcake cups with liners (split them among two trays). Or, line two 9x2-inch round pans with parchment.
Combine the wet ingredients in a bowl; combine the dry ingredients except for the chocolate chips in another. Set aside.
Using a flexible spatula, toss two tablespoons of the wet ingredients with the chocolate chips in a small bowl. Add 1/4 cup of the dry ingredients. Toss again to coat evenly.
Mix the butter and sugars in the bowl of a standing mixer with a paddle attachment until the combination is well creamed--about 3 minutes.
Add the egg and yolk, one at a time.
Alternately add the dry and wet mixtures, about a quarter each at a time, without pausing between additions. Ease the resistance against the mixer's paddle by lowdering the bowl or raising the mixer's head.
Remove the bowl and fold in the chocolate chips with the flexible spatula, using the handle if necessary. This mixture will be thick--more like cookie dough than cake batter.
Divide the dough into your prepared pans or cupcake cups. If you're using pans, it will be too thick to spread to the edges, but the oven's heat will spread it for you. If you're using cupcake cups, put a heaping spoonful (or ice cream scoop's worth) of batter in each cup.Bake for 20 to 24 minutes for a cake--for cupcakes, I found that about 30 minutes was more like it. The edges will crown slightly, and become crispy. The tops should be evenly browned.
Cool the cakes in the pans to room temperature, then if you're making cakes, invert them, using a small offset spatula to release the edges; if you've made cupcakes, just remove them from the pan.
Prepare chocolate icing.In a saucepan over medium heat, bring the cream and sugar to a light simmer, stirring occasionally. Place the butter, chocolate, and vanilla in a large bowl. Pour the hot cream over the ingredients in the bowl and let stand for a few minutes to melt the chocolate. Whisk until smooth and set aside to cool, but do not refrigerate. Once the icing has thickened, stir with a flexible spatula until it reaches a spreadable consistency. Choose your adventure on assembly in the next step.
Spread either between cake layers, leaving the top bare or sprinkled with confectioners' sugar and chocolate chips; if you're making cupcakes, spread frosting on top, or remove cupcakes from cups, split in half and fill with frosting and top with confectioners' sugar and chocolate chips as in the case of the cake.