Combine whole-wheat flour, all-purpose flour, yeast and salt in a stand mixer with the dough-hook attachment. Add 2 eggs, milk, sugar (or honey) and 2 tablespoons softened butter. Mix on low speed until the dough has pulled together and is smooth and elastic, about 6 minutes.Advertisement
Coat a large bowl with cooking spray. Scrape the dough into the bowl (it will be sticky) and turn to coat. Cover with plastic wrap. Let rise in a warm place until doubled in volume, about 1 hour.
Punch the dough down and turn it out onto a lightly floured surface. Divide into 3 equal pieces. Roll each piece out into a 1-inch rope about 14 inches long. Loosely braid the 3 ropes together, leaving spaces for the 6 whole eggs.
Transfer the braid to a baking sheet lined with parchment paper. Nestle the eggs into the braid, spacing evenly. Cover loosely with plastic wrap. Let rise in a warm place until doubled in bulk, about 45 minutes.
Preheat oven to 350 degrees F.
Melt the remaining 1 tablespoon butter and brush the dough with half of it. Bake the bread until golden brown, 30 to 45 minutes. Transfer to a wire rack, brush with the remaining melted butter and let cool for at least 30 minutes. Serve warm or at room temperature.
Tip: Many farm-fresh eggs come in a variety of colors including blue, green and brown. If you can't find colored eggs, naturally dye your own with these instructions: http://www.eatingwell.com/healthy_cooking/healthy_cooking_101_basics_techniques/how_to_dye_eggs_with_natural_dyes
1 1/2 starch, 1/2 fat, 1/2 medium-fat protein