Preheat the oven to 425 degrees F. Toss the squash with 1 tablespoon olive oil on a rimmed baking sheet; season with salt and pepper. Bake, tossing halfway through, until golden brown and tender, about 20 minutes. Transfer to a plate and let cool. Add the bread to the baking sheet and bake until lightly toasted, 8 to 10 minutes; transfer to a large bowl.
Meanwhile, heat the remaining 3 tablespoons olive oil in a large skillet over medium heat. Add the salami and cook, stirring, until lightly browned, about 5 minutes. Remove to a paper towel-lined plate with a slotted spoon, reserving the drippings in the skillet.
Add the sliced fennel and celery to the skillet and cook, stirring, until softened and browned, about 10 minutes. Add the chicken broth, vinegar, 1/2 teaspoon salt and a few grinds of pepper; cook, stirring, until the liquid is slightly reduced, about 3 minutes. Remove from the heat and stir in the roasted peppers and marjoram.
Pour the fennel mixture over the bread cubes and let sit 2 minutes. Add the squash and salami and toss to coat. Top each serving of panzanella with the asiago and fennel fronds.