Preheat the oven to 350°F.

Grease and flour an 8-inch square baking pan.

In a double boiler or heatproof bowl over simmering water, melt the chopped semi-sweet chocolate and butter, stirring until smooth.

Remove from heat and cool to room temperature.

Stir in brown sugar and vanilla extract into the chocolate mixture.

Add eggs, one at a time, mixing well after each addition.

Sift together flour, baking powder, and salt in a separate bowl.

Gradually fold the dry ingredients into the chocolate mixture until well blended.

Stir in the bittersweet chocolate chips.

Pour the batter into the prepared pan.

Bake for 25 to 30 minutes, until a tester inserted in the center comes out clean.

Cool in the pan for at least 10 minutes before slicing into squares.