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In a medium saucepan, combine the milk, 1/2 cup of water, and the butter, and bring to a simmer over medium heat. Add the flour, stirring with a wooden spoon until a dough forms into a ball, leaving a thin coating of cooked flour on the bottom of the saucepan, 2 to 3 minutes. When you hear the dough begin to sizzle very softly, it has been cooked and stirred enough. Carefully transfer the hot dough to a stand mixer fitted with the paddle attachment. Mix on medium-low speed and, with the mixer running, add the eggs one at a time. Continue mixing until the dough is shiny, thick, and falls in golden ribbons from the paddle, 1 to 2 minutes.
Transfer the dough to a large pastry bag fitted with a large star tip (or a resealable bag with a corner snipped off). Combine the sugar and ground anise seed in a medium shallow bowl for coating the xurros.
In a small saucepan, toss together the chocolate and cornstarch. Place over medium-low heat and stir constantly until the chocolate begins to melt and soak up the cornstarch. Gently whisk in the milk and cook until the chocolate coats the back of a spoon, about 5 minutes. Stir in the sugar and vanilla until the sugar dissolves. Cover and set aside to keep warm.
Heat 2 inches of oil in a large Dutch oven over medium heat to 350°F. Adjust the heat as necessary to maintain the 350°F frying temperature. To form each xurro, pipe the dough into the hot oil in a loose swirl. Fry until puffed and golden brown on both sides, about 4 minutes, flipping once. As they are done, transfer the xurros to paper towels to drain briefly. While still warm, toss the xurros in the spiced sugar.
Pour the hot chocolate into small mugs and serve warm with the xurros on plates or a platter.
