Heat a large saute pan over medium-high heat. Melt the butter and 2 tablespoons of olive oil together, then add the onion and a pinch of salt. Cook for 5-7 minutes, until the onions are translucent.

Add the fennel and mushrooms, another pinch of salt, then cook for 2-3 more minutes. Add the carrots and celery, and continue to cook, stirring occasionally, until the vegetables are softened and reduced in volume, about 10 minutes. Remove from the heat and set aside to cool briefly.

Preheat the oven to 375°F. Prepare a 9x13 baking dish by brushing with butter or olive oil. Set aside.

In a large bowl, combine the broth, red wine vinegar, and eggs, whisking to combine. Add the cooled vegetables and herbs, a pinch of salt and pepper, and stir. Add the dry or stale bread, then toss well until each bread is coated. Pour into the prepared baking dish, then drizzle the top with the remaining olive oil.

Bake for 45-60 minutes, until golden brown on top. Serve while warm.80