To make either version of the brownies, melt together the chocolate and butter. Stir until smooth and then cool.
Whisk in the sugar by hand, followed by the eggs, one at a time.
Stir in the vanilla and then the flour. You can add toasted nuts as well, if you'd like.
Pour into a greased and lined pan (8" x 8" for thicker brownies and 9"x 13" for thinner brownies) and bake at 325°F until done.