In the bowl of a food processor, add the flours, yeast, sugar and salt and pulse to combine. Add the rosemary and pulse to combine. Add the olive oil to the water and with the processor running, add the water through the feed tube. Process for 1 minute to knead the dough. It should be in a ball. Remove to a lightly floured board and knead 2 or 3 times. Cover with a bowl and let rest for 10-15 minutes.
Preheat oven to 400 degrees F. Line a baking sheet with parchment paper and set aside. Cut the dough ball into 2 and using your fingers spread out to about 12 inches long. Make a dent down the center lengthwise and fold the long side closest to you into the middle. Fold the 2/3 section over the back side making a long rope with a seam lengthwise. Place on the parchment lined sheet seam side down and repeat with remaining dough.
Bake for 20-25 minutes or until the baguette sounds hallow when thumped. Remove and let cool completely before slicing. Turn the oven down to 350 degrees F. Cut the baguettes into cubes and add back to the parchment lined baking sheet and bake for 25 minutes. Remove and let cool. Add to a large bowl and set aside.
Stuffing
Preheat oven to 400 degrees F.
In a large skillet over medium high heat, melt the butter. Add the sliced onions and 1 teaspoon of salt. Toss to coat with butter. Turn the heat down to medium and saute the onions, stirring occasionally, until they are golden brown. If they begin to burn, turn down the heat a bit. Add the onions to the bowl with the toasted bread cubes.
Add the mushrooms to the large skillet and season with salt and pepper. Saute until they begin to brown, about 5 minutes. Remove to the bowl with the bread mixture. Add the rosemary to the bowl. Turn the burner up to high and add the chicken stock to the skillet. Scrape up any browned bits on the pan and then pour into the bread mixture. Add 2 eggs and toss all to combine. Season with salt and pepper to your taste.
Spray a 9×13 inch baking dish with cooking spray (or butter generously) and add the stuffing. Cover tightly with foil. Bake for 30 minutes then remove the foil and bake for another 30 minutes. Remove and serve immediately.