Place your oven rack in the middle position. Preheat the oven to 190°C (375°F). Butter a sheet of parchment paper and use it to line an 8 x 8-inch square baking pan, letting the parchment paper hang over the sides.
In a pot or in the microwave, melt the chocolate and butter over medium-high heat and stir well. Remove from heat.
Add the brown sugar and egg and whisk with a fork. Using a wooden spoon, stir in the flour. Pour into the baking pan.
In a bowl, combine the flour, baking soda, and salt.
In another bowl, whisk the brown sugar and butter with an electric beater. Whisk in the egg and vanilla. Incorporate the dry ingredients with a wooden spoon, then fold in the chocolate. Pour the cookie batter on top of the brownie batter.
Bake in the oven for approximately 20 minutes. Let cool. Unmould and cut into squares.