Using a wooden spoon or a stand mixer fitted with a dough hook, mix the flour, yeast and salt. Add the eggs and milk mixture and mix vigorously until the dough starts to form. Gradually add the softened butter. Knead the dough for about 5 minutes using the stand mixer, or by hand on a floured work surface. Transfer the dough to a clean, lightly oiled bowl. Cover with a slightly damp cloth and let stand in a warm, humid place for about 15 minutes.
On a well-floured work surface, roll out the dough to form a 35 x 50-cm (14 x 20-inch) rectangle. Brush with melted butter. Set aside.
In a bowl, combine the brown sugar and spices. Sprinkle over the dough. Roll the dough tightly into a log about 50 cm (20 inches) long.
Using a sharp knife, cut the log into 12 slices. Arrange the slices in a buttered 23 x 33-cm (9 x 13-inch) glass baking dish, leaving space between each bun. Let rise uncovered in a warm, humid spot until the buns are touching, about 90 minutes.
With the rack in the middle position, preheat the oven to 180°C (350°F). Bake for 25 minutes or until the buns are golden.
In a bowl, combine the icing sugar and milk. When ready to serve, glaze the buns.
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Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.