Make the filling: Beat together the cream cheese, granulated sugar, and egg until smooth. Stir in the chopped chocolate pieces. Set aside.
Make the cupcakes: Adjust the rack to the center of the oven and preheat to 350°F (175°C). Butter a 12-cup muffin tin, or line the tin with paper muffin cups.
In a medium bowl sift together the flour, brown sugar, cocoa powder, baking soda, and salt. In a separate bowl, mix together the water, oil, vinegar, and vanilla.
Make a well in the center of the dry ingredients and stir in the wet ingredients, stirring until just smooth. Stir any longer and you will over mix the batter and end up with less-than-tender cupcakes.
Divide the batter among the muffin cups. Spoon a few tablespoons* of the filling into the center of each cupcake, dividing the filling evenly. This will fill the cups almost completely,** which is fine.
Bake for 25 minutes, or until the tops are slightly golden brown and the cupcakes feel springy when gently pressed. These moist treats will keep well unrefrigerated for 2 to 3 days if stored in an airtight container.
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