Preheat the oven to 400 degrees F. Toss the bread cubes and 1 tablespoon olive oil in a bowl. Spread on a rimmed baking sheet and bake, tossing occasionally, until crisp, 8 to 10 minutes. Let cool.
Meanwhile, toss the giardiniera in a large bowl with the basil, olives, peppers, romaine, mortadella, prosciutto, capicola, salami, provolone and the remaining 1 tablespoon olive oil. Drizzle with the giardiniera brine and toss. Let sit about 20 minutes to let the flavors combine.
Add the croutons to the salad and toss. Divide among bowls.