Preheat oven to 350°. In a medium pot, bring 1 in. water to a simmer. Put chocolate and butter in a medium metal bowl and set bowl over pot, being careful not to let bottom of bowl touch water. Heat until chocolate is almost completely melted, then add sugar and eggs and mix thoroughly. Sift together flour, cocoa, and salt, then add to chocolate mixture, stirring well. Pour batter into a greased 10- by 15-in. baking pan. Bake until a toothpick inserted in center comes out clean, about 20 minutes. Let cool completely.
Invert brownie sheet onto a work surface and cut into 1 1/2-in. squares; arrange on pan. Freeze brownies 30 minutes. During last 5 minutes, remove ice cream from freezer to soften.
Working in batches, scoop 1 heaping tbsp. ice cream onto half of brownie squares. Set remaining squares, shiny side up, on top of ice cream and press gently.
Freeze until firm, at least 2 hours. Straighten tops of brownies and trim oozing ice cream with a paring knife if you like. Freeze, covered, up to 1 week.
Note: Nutritional analysis is per sandwich.