Preheat the oven to 350 degrees. Coat a 9-by-13-inch baking dish with cooking spray.
Melt the chocolate and butter in a heatproof bowl set over a saucepan of barely simmering water, stirring occasionally; do not let the bottom of the bowl touch the water.
Whisk the flour, cocoa, salt and baking soda in a medium bowl. In a large bowl, whisk the eggs and brown sugar until smooth, then add the yogurt, oil and vanilla and whisk to combine. Whisk in the melted chocolate mixture until blended. Add the dry ingredients and mix until just moistened.
Spread the batter in the prepared pan and sprinkle with walnuts, if desired. Bake for 20 to 25 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs. Cool completely in the pan on a rack before slicing.