Preheat oven to 375°F. Lightly butter an 8-inch square baking pan. Put chopped chocolate in a medium-size microwave-safe bowl. Microwave on high for 1 minute. Stop, stir and microwave for 30 seconds longer. Stir and set aside to cool slightly.
Beat butter and sugar until fluffy. Add eggs, one at a time, beating after each addition. Stir in melted chocolate, vanilla and salt; mix well. Fold in flour and baking powder.
Pour batter into prepared pan, spread evenly and bake until a toothpick inserted in center comes out clean, about 30 minutes.
While brownies are still warm, sprinkle marshmallows and chocolate chips on top. Return to oven for 2 minutes to melt toppings. Serve with ice cream, if desired.