Pre-heat the oven to 500°F.
Drizzle the pork tenderloin and the chicken breasts with EVOO and sprinkle with the seasoning blend, salt and pepper. Place the pork on a rack set over a rimmed baking sheet and roast in the oven for 10-12 minutes. Reduce the heat to 425°F and roast until a thermometer inserted into the thickest part of the pork registers 145-155°F, about 15 more minutes (do not open the oven while it’s cooking). Transfer the pork to a cutting board and let rest for 5 minutes, if desired. Then very thinly slice on an angle.
Meanwhile, heat a cast iron skillet or griddle over medium-high heat. Add the chicken and cook, flipping occasionally, until firm but not tight and the juices run clear, 12-15 minutes. Transfer to a cutting board and let rest for 5 minutes, if desired. Then thinly slice on an angle.
Pulse the giardiniera in a food processor until finely chopped.
Layer the chicken and pork on the rolls and top with the cheese, lettuce, tomato and red onion. Scatter the giardiniera relish over the top, then drizzle with the hoagie dressing (instructions below).
To make the hoagie dressing, in a mixing bowl, combine the vinegar, herbs, sugar, garlic, shallot, chili pepper and lemon juice. Whisk in the EVOO in a slow stream. Add the mustard and season with salt and pepper, then whisk until emulsified.