Preheat the oven to 350 degrees F. Toss the bread with 1/4 cup olive oil and half of the garlic in a large bowl. Divide between 2 baking sheets and spread in a single layer. Bake until crisp and golden, 20 to 25 minutes. Let cool.
Heat the remaining 1/4 cup olive oil in a large deep skillet over medium-high heat. Add the red onions, salami and soppressata and cook, stirring occasionally, until the onions are softened, about 6 minutes. Add the giardiniera, oregano and the remaining garlic and continue to cook, stirring occasionally, until the garlic starts browning, 2 to 3 minutes. Add the chicken broth and bring to a simmer.
Combine the toasted bread and broth mixture in a large bowl and gently mix until all the bread is moistened. Stir in the beaten eggs, provolone and parsley.
Brush a 3-quart baking dish with olive oil. Add the stuffing and dot with the butter. Cover with foil and bake 30 minutes. Uncover and continue to bake until golden brown, 20 to 30 more minutes.