Step 1Place the milk in a medium saucepan with the chocolate and one-fourth cup sugar. Cook over medium heat until the chocolate and sugar are dissolved, stirring to blend in the chocolate, about 5 to 10 minutes. Strain through a fine-mesh sieve into a large bowl and stir in the whipping cream. Set aside.
Step 2Place the remaining 1 cup sugar in a large skillet over high heat. When the sugar starts to melt, reduce the heat to medium and cook, stirring occasionally, until the caramel is clear and golden brown, about 5 to 7 minutes. Quickly spoon the caramel over the bottom and around the sides of a glass 8-inch round cake dish. Set aside until firm.
Step 3Lightly whisk the egg yolks, then mix them into the milk mixture. Pour into the baking dish, place in a pan of hot water and bake at 325 degrees until a knife inserted in the center comes out clean, about 1 hour. Place on a rack to cool slightly, then refrigerate at least 3 hours or overnight. Gently release the flan from the dish by running the tip of a knife around the edge. Use your fingers to gently pull the sides away from the edge. Place a serving platter on the cake dish and invert the flan onto the platter.