Preheat your grill to medium-high heat. You want the temperature around 400 to 425 degrees F. Spray or brush a 9x13 inch baking dish (or roasting pan) with the melted butter.
Brush both sides of the italian bread slices with olive oil. Once the grill is hot, place the bread on the grates. Grill on both sides until charred and grill marks appear, about 1 to 2 minutes per side. Let the bread cool completely. Once cool, tear or chop the slices into pieces.
Preheat the oven to 350 degrees F. Toss together the sourdough pieces of bread and the grilled pieces of bread in the buttered baking dish.
Heat a large skillet over medium heat and add the butter. Once melted, stir in the onion, celery, garlic, salt and pepper. Cook, stirring occasionally, until the veggies soften, about 5 to 6 minutes.
Pour the entire butter/onion/celery mixture over the bread pieces in the baking dish. Add the fresh herbs on top. Add in 1 cup of stock. Toss everything together.
In a small bowl, whisk together the eggs and remaining stock. Pour it over the bread and mix everything well to combine. I like to mix very well so there are no big spots of egg anywhere.
Place the stuffing in the oven and roast for 60 to 75 minutes. You want the internal temperature of the stuffing to be 160 degrees F when tested with a thermometer. If the edges start to burn too much, you can tent the stuffing with foil.