Preheat to 350°F (175°C) and adjust the rack to the center of the oven. 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 just until smooth. Don't overmix or you'll end up with less-than-tender and actually quite tough cupcakes.
Divide the batter evenly among the muffin cups. Spoon a few tablespoons of the cream-cheese filling into the center of each cupcake. The cups will be almost completely filled.
Bake the cupcakes for 25 minutes, or until the tops are lightly golden brown and the cupcakes feel springy when gently pressed. These will keep in an airtight container at room temperature for 2 to 3 days.