Preheat oven to 350°. In a double boiler over simmering water, melt chocolate and butter (see "Melting Chocolate the Easy Way," below, for another method). Stir in brown sugar and vanilla. Take off heat. Add eggs and mix thoroughly. Add flour, cocoa, and salt, mixing until smooth. Stir in chocolate chips.
Pour batter into an 8-inch square pan. Bake until a toothpick or knife inserted in the center comes out with moist crumbs sticking to it, 20 to 25 minutes.
Melting chocolate the easy way: Double boilers are great for gently melting chocolate, but we've found an even easier method that uses common kitchen equipment. Put chopped chocolate in a small metal bowl along with any other ingredients you need to melt, such as butter. In a large frying pan over high heat, bring about an inch of water to a low boil. Take pan off the heat and set the bowl in the water. Let sit, stirring occasionally, until chocolate is melted, 5 to 10 minutes.
Note: Nutritional analysis is per 2-inch brownie.