Line an eight-inch square baking pan with wax paper. In a heavy medium saucepan, whisk together sugar and cocoa. Add cream, butter, and corn syrup; cook over medium-high heat, stirring, until bubbling around the edges, about five minutes.
Continue cooking, without stirring, until mixture reaches the soft-ball stage on a candy thermometer (238 degrees to 240 degrees), 12 to 15 minutes; wash down sides of pan with a pastry brush dipped in water to prevent crystals from forming.
Remove pan from heat; let mixture rest in pan, undisturbed, until it has cooled to 160 degrees, about 40 minutes.
When temperature reaches 160 degrees, quickly pour fudge onto surface, using a rubber spatula to gently empty pan while holding pan very close to surface to prevent spattering. Spoon vanilla extract over fudge; let cool until fudge is almost at room temperature, about 15 minutes.
Using a long offset spatula, being pulling fudge in a figure-eight motion, moving from the bottom right, then up and over to the top left, before pulling back down to the right. Repeat, moving from the bottom left, then up and over to the top right, before pulling back down, pushing fudge onto itself.
Continue in this manner until you see a sudden change in appearance of fudge, from glossy to matte, 12 to 15 minutes. Sprinkle with chopped nuts, if desired, and stir well to combine.
Spread fudge onto a wax-paper-lined baking sheet; flatten with lightly buttered fingertips. Cover with wax paper; let stand at room temperature until set, at least four hours or overnight. Cut into squares before serving.