Preheat oven to 325°F. Grease a 9x9-inch baking dish.
In a double boiler over not-quite-simmering water, melt chocolate and butter and stir until smooth. Cool slightly. Stir in sugar. Add eggs, one at a time, beating thoroughly. Stir in vanilla, then add flour and nuts (if using). Spread in prepared pan and bake for 40 minutes. Cool in the pan.
Chocolate Peppermint Brownies
Bake brownies as above, then arrange 10-20 chocolate peppermint patties over the hot brownies; return to the oven for about 3 minutes to soften. Then spread to cover the entire top of the brownies. Cool and cut.