Preheat oven to 350°. Chop the chocolate into small pieces, place in a small heavy-bottomed pan and heat over low heat, stirring constantly, until melted. Remove from heat.
Using an electric mixer, beat butter and 2 cups sugar at medium speed until light and fluffy. Add eggs one at a time, waiting until each egg is blended in before adding the next one.
Add melted chocolate, and beat just until blended. Add flour and 1 teaspoon vanilla extract and beat on low speed until flour is moistened.
Spread batter into 9X13-inch pan. Sprinkle semi-sweet chocolate chips on top and bake for 30 minutes if using a metal pan and slightly longer in a glass pyrex dish.
Sprinkle marshmallows on top of brownies and return to oven on top rack for 1-2 minutes or until marshmallows are melted and lightly browned on top.
Combine peanut butter and canola oil in a small bowl and microwave for 10 seconds on HIGH. Stir to combine and drizzle on top of marshmallow covered brownies.
For chocolate frosting, combine ¼ butter, unsweetened cocoa, and milk in a saucepan and cook over medium heat, stirring constantly for 2-3 minutes.. Whisk in powdered sugar and vanilla extract until smooth. Drizzle on top of brownies.