Make the Dough: Whisk the milk, eggs, and melted butter together in the bowl of a stand mixer. With a wooden spoon, stir in the flour, granulated sugar, yeast and salt until just combined (the mixture will be fairly dry and shaggy). Attach the bowl to a stand mixer and fit with the dough hook. Mix on medium-low speed for 10 minutes (the dough will be soft and slightly tacky). Transfer the dough to a greased bowl, cover tightly with plastic wrap, and let rise at room temperature until doubled in size, 1½ to 2 hours.
Assemble the Cake: Grease a 12-cup nonstick Bundt pan. In a medium bowl, combine the pecans, brown sugar, and cinnamon. Roll out the dough into an 18 by 14-inch rectangle on a lightly floured surface, with the long side parallel to the counter edge. Spray lightly with water (or sprinkle with water and lightly spread it around with your fingers), and sprinkle evenly with the pecan mixture. Roll the dough away from you into a log and pinch along seam to seal. Form into a ring and seal the ends together. Place seam side up into the prepared Bundt pan, cover loosely with plastic wrap, and let rise at room temperature until doubled in size, about 1 hour.
Adjust oven rack to middle position and heat oven to 350 degrees.
Bake until deep golden brown and cake registers 190 degrees in the center on an instant read digital thermometer, 30 to 35 minutes, rotating halfway through baking. Let the cake cool in the pan for 10 minutes, then remove the cake from the pan and transfer to a wire rack, seam side down, and let cool completely, about 2 hours.
Make the Topping: Whisk the powdered sugar and 3 tablespoons milk together in a bowl until smooth. Pour over the top of the cooled cake. Sprinkle one-sixth of the top with half of the yellow sugar, then repeat on opposite side. Repeat with green and purple sugars to form alternating bands of color. Serve at room temperature. Leftovers should be wrapped tightly or stored in an airtight container for up to 3 days.