Preheat the oven to 350 degrees F.
Put the ground beef and pork in a large bowl and douse with the wine. Grate 3 to 4 tablespoons onion directly into the bowl to catch the juices. Add the oregano, garlic, chile, cheese, 1 tablespoon pepper and a drizzle of EVOO. Mix until just combined. Shape into 4 large patties or 12 small patties for sliders. Make an indentation in the center of each patty to help them cook evenly and prevent them from puffing up. Sprinkle with a little salt.
Arrange the salami slices on a rack set over a rimmed baking sheet. Bake until they crisp up a bit, about 10 minutes. Let cool.
Heat a heavy griddle or cast-iron skillet over medium-high heat. Add the patties and cook, turning occasionally, about 10 minutes for regular ones and 6 minutes for sliders. Top with the provolone and cook until melted.
Spread some of the giardiniera relish on the bottom halves of the rolls and top with the patties. Top with the salami and some Quick Marinara Sauce. Cover with the top halves of the rolls.
Heat the EVOO in a small pot over medium to medium-high heat. Add the garlic, chile and onion and cook, stirring, 1 to 2 minutes. Add the wine and cook 30 seconds. Add the tomatoes, oregano, basil and thyme. Season with salt and pepper. Simmer over low heat until thickened.