Preheat oven to 350F. Line an 8x8x2-inch baking pan with parchment paper, leaving about 1 inch of the paper extending over the ends of pan. Grease paper; set pan aside.
In a medium saucepan, stir together butter and unsweetened chocolate over low heat until smooth; set aside to cool.
Stir the sugar into the cooled chocolate mixture.
Add the eggs, 1 at a time, beating with a wooden spoon just until combined.
Stir in vanilla.
In a small bowl stir together the flour and baking soda.
Add flour mixture to chocolate mixture; stir just until combined. If desired, stir in nuts. Spread the batter evenly in the prepared pan.
Bake in the preheated oven for 30 minutes.
Cool in pan on a wire rack. Remove brownies from pan, using the overlapping paper to lift brownies. Place on cutting board; cut into brownies as desired.