To make the dough: Gently heat the milk in a small saucepan to slightly warmer than body temperature (105 to 110 degrees F). Pour the milk into a bowl, sprinkle the yeast over the surface, and add a teaspoon of the sugar and a tablespoon of the flour. Stir to combine, and let the yeast plump with the milk before whisking. Set aside to proof for about 10 minutes.
In a mixing bowl, with the paddle attachment on a heavy-duty mixer, cream together 11 tablespoons of the butter and the remaining sugar until light and fluffy, 1 to 2 minutes. Add the yeast mixture and mix for 1 minute. Add an egg and mix thoroughly; follow with a third of the flour. Repeat with the remaining eggs and flour. Add the lemon zest and salt, and continue to mix on low speed for 8 to 9 minutes, until the dough is smooth, shiny, and elastic, and pulls away from the side of the bowl. If very soft, add up to 1/2 cup of flour. Scrape the dough from the mixing bowl and knead lightly to form a ball. Butter a medium-size bowl with the remaining tablespoon of softened butter. Transfer the dough to the bowl and turn it in the bowl to coat with the butter. Cover with plastic and set in a warm spot to proof for 1 hour, or until doubled in bulk.
After an hour, turn the dough out of the bowl, punch it down, and knead lightly to form into a ball. Put the dough back in the bowl, covered, and refrigerate for at least 2 hours or for up to 24 hours.
To form the cake: flour a clean work space and roll the dough into a 20-x-10-inch rectangle, keeping the thickness consistent throughout. If the edges get thin, trim them to keep consistent. Cut the dough lengthwise into 3 strips. Paint each strip of dough with the melted butter, leaving a 1/2-inch border clean along the length of each of the strips. (Reserve any leftover butter for brushing on the cake before baking.) Sprinkle the butter with the brown sugar and cinnamon.
Line a baking sheet with parchment. Fold each strip over, lengthwise and toward the clean edges, to enclose the cinnamon and sugar, and pinch the seam to seal the dough closed. Braid the 3 rope like pieces together. Transfer the braid to the baking sheet, and form the braid into a wreath by pressing the ends together. Cover with a towel, and set aside to proof for 40 minutes. Preheat the oven to 350 degrees F.
Brush the cake with the reserved melted butter, and bake for 20 minutes, until golden brown. Tent the cake with foil and continue baking for 25 minutes. Keeping the cake on the baking sheet, cool on a rack. After the cake has cooled, carefully tuck the bean or almond into the underside of the cake.
To make the icing: Whisk the confectioners' sugar with the water in a medium saucepan and heat very gently to dissolve the sugar. Divide the icing into 3 small bowls and add the food coloring to make a mild green, a golden yellow, and a purple (1/2 drop red and 1/2 drop blue). Brush the ridges of the dough while it is still warm with alternating Mardi Gras colors. Cool and serve.
Be very careful not to swallow the bean or the almond. Be especially careful with children.
Recipe courtesy of Gatherings and Celebrations, by Burt Wolf, Doubleday, 1996