For the chicken: Preheat the oven to 200 degrees F. Set a wire rack inside a baking sheet.
Heat the oil over medium heat in a heavy-bottomed skillet. Sprinkle the chicken with salt and pepper. Dredge in the flour and shake off any excess. Fry the chicken in the oil until golden brown, 5 to 6 minutes a side. Set aside on the prepared baking sheet. Keep warm in the oven. Slice the chicken in half before assembling the sandwiches.
For the chicken jus: Add the oil into the same skillet from the chicken and saute the Italian seasoning, crushed red pepper, garlic and shallots until fragrant, about 1 minute. Season with salt and pepper. Deglaze with the white wine and bring to a simmer until the alcohol smell is diminished, about 2 minutes. Add the chicken stock and lemon juice and bring to a simmer again, about 10 minutes until the flavor intensifies. Keep warm for sandwich build.
For the peas and mushrooms: Heat half the oil in a heavy-bottomed skillet and saute the mushrooms without overcrowding or creating layers. You may have to do this in batches. Give the mushrooms one stir and let caramelize. Once one side is golden brown, season with salt and pepper, stir once and let cook until all sides are soft but golden. Remove to a plate. To the same skillet, add the remaining oil and the peas. Season with salt and pepper. Cook until warm but still very bright. Mix with the mushrooms and set aside.
For the sandwich build: On a nice fresh piece of split but hinged French roll, place a squirt of good mayo, 2 slices provolone, 2 Roasted Potato Wedges, 1 chicken breast, some mushroom and peas and top with hot giardiniera. Take the entire sandwich and either dunk in hot chicken jus or ladle on. Hold with one or two hands and bite hard.
Roasted Potato Wedges:
Preheat the oven to 475 degrees F.
Toss the potato wedges with the olive oil, garlic powder, salt and pepper in a bowl. Lay the potatoes on a baking sheet and cook until golden brown on each side, flipping halfway through, about 12 minutes per side. When both sides are golden and the potatoes can be pierced easily with a fork, the taters are done.