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Line 2 baking sheets with parchment. Draw 2 sets of pencil lines 3” apart on each paper and then turn the parchment over.
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In a medium saucepan, combine butter, water, milk, sugar and salt. Cook over medium heat until the butter has melted and it just comes to a boil. Reduce the heat to low and add the flour, stirring and smearing the dough vigorously with a wooden spoon for 3 minutes. The dough should thicken and start to make a ball. Remove the pan from the heat and let cool 5 minutes.
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Add the eggs to the dough in 3-4 additions, beating well between each addition. The batter should be shiny and thick. Using a piping bag and a ½”star tip, pipe between the 3” marks on the parchment, leaving room between each for expansion. Bake at 425°F for 15 minutes and then reduce the oven temperature to 350° (do not open the oven) and bake 10-15 minutes until nicely brown. Remove the eclairs from the oven and using a skewer, poke a hole in each end to release any steam.
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For the filling: in a medium bowl, beat the egg yolks and milk. In a medium saucepan, combine the cornstarch, cocoa powder, sugar and salt. Gradually whisk in the egg/milk mixture. Cook over medium heat, stirring constantly until the mixture thickens and comes to a boil. Remove from heat and pour into a bowl. Stir in the peppermint extract and press a piece of plastic to the surface to prevent a skin from forming. Refrigerate until thoroughly cool (at least 1 hour).
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For the chocolate glaze: in a small bowl, combine the chocolate, butter, water and corn syrup. Melt the mixture in the microwave in increments of 30 seconds at 50% power until melted.
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To serve: using a piping bag with a small tip, fill each éclair from either end or by filling with three holes in the bottom. Arrange in a wreath shape on a round platter. Drizzle with the chocolate glaze and sprinkle with the crushed candy canes.
