Heat the milk in a small saucepan until it just begins to simmer, then remove from the heat and let cool to 115 degrees F. Stir in the yeast and let stand until the mixture is foamy, about 10 minutes.
Pour the yeast mixture into the bowl of stand mixer fitted with a dough hook. Add the sugar, butter and 2 of the eggs and stir until smooth. Add the flour and salt and mix on medium-low speed until the dough comes together. Increase the speed to medium high and knead until the dough is smooth and elastic, about 8 minutes. Transfer the dough to a lightly greased large bowl, cover with plastic wrap and let stand until the dough doubles in size, about 1 hour.
Preheat the oven to 350 degrees F and line a rimless baking sheet with parchment.
Turn the dough out onto a lightly floured work surface. Pinch off 1 golf ball-size piece of dough and roll it into a ball for the pompom of Santa's hat. Pinch off 1 ping pong ball-size piece of dough and roll it into a ball for Santa's nose. Cut off a 1-inch-wide, 9-inch-long, 1/4-inch-thick strip and roll it into a smooth log for the brim of Santa's hat. Cut another piece of dough into a roughly 2-inch-wide, 5-inch-long, 1/4-inch-thick strip of dough. Snip evenly from the bottom (but not all the way up) and spread the strips out slightly to form a mustache.
Roll out the remaining dough into an elongated diamond with the top triangle of the diamond double the length of the bottom triangle. Position the diamond on the prepared baking sheet with the top of the longer triangle hanging over the edge. Working on the shorter triangle, use scissors or a knife to cut 1/2-inch-wide strips of dough up toward the middle, stopping at the imaginary line where the top and bottom triangles meet. Pick up each strip of the beard and twist it, if you like, lying the twists down next to each other naturally so they look like a beard.
Fold over the overhanging corner of dough so that it fits back within the edge of the baking sheet and position it slightly to the right to form the tip of Santa's hat. Position the dough log across the top triangle where the tip of Santa's hat ends and tuck the ends under the sides of the triangle; this is the brim of Santa's hat. Position the golf ball-size ball of dough over the tip and against the brim and press lightly to adhere for the pompom of Santa's hat. Arrange the mustache at the top of the beard, then position the ping pong ball-size ball of dough above the mustache to make Santa's nose.
Beat the remaining egg with the cream in a bowl to make an egg wash. Using a pastry brush, brush the entire surface of the dough, including the pompom and brim of the hat but not the body of the hat, with the plain egg wash, making sure to get into all the crevices of the shapes. Add the food coloring to the egg wash, stir to combine, then carefully brush the body of the hat with the red egg wash, being careful not to let it stain the pompom or brim.
Bake until the bread is golden brown and cooked through, about 20 minutes. Remove from the oven and immediately set the chocolate chips proportionally on either side and slightly above Santa's nose to form his eyes. Let the bread cool for 10 minutes on the baking sheet, and then transfer to a wire rack. Using cut pieces of parchment paper or foil to shield Santa's nose, face and the body of his hat, dust the beard, brim and pompom with confectioners' sugar. Remove the paper and serve the bread while still warm with butter.