In a large bowl, combine flour, salt, and yeast. Drizzle in water, and honey and stir dough with a wooden spoon until a slightly-sticky dough forms. Cover bowl with plastic wrap and let sit at room temperature overnight or 18-24 hours.
The next day, preheat oven to 425F. Lightly grease a baking sheet and set aside. In a medium skillet, caramelize onions in butter over medium heat, stirring occasionally until onions are a deep golden brown. Remove from heat and cool completely.
Punch risen dough down and gently knead caramelized onions into dough. Gather dough into a smooth ball and place on prepared pan. With a sharp knife, cut a few slits in the top and brush with beaten egg and sprinkle with asiago cheese. Let rise 30 minutes until doubled in size.
Bake bread at 400F 30-35 minutes or until bread is a deep golden brown. Cool loaf on a wire cooling rack slightly then slice and serve warm. Enjoy!