Step 1

Season 1 (3- to 4- pound) top round roast all over with 1 teaspoon kosher salt if using regular beef broth (or 1 1/2 teaspoons if using low-sodium beef broth) and 1/4 teaspoon black pepper.

Step 2

Heat 4 teaspoons olive oil in large skillet or Dutch oven over medium-high heat until shiimmering. Add roast and sear until browned and crusty on all slides, about 10 minutes total. Transfer the roast to a 5-quart or larger slow cooker.

Step 3

Add 1/4 cup water to the pan, scraping up the browned bits with a wooden spoon. Pour into the slow cooker. Add 2 cups beef broth, 1 (0.7-ounce) package Italian salad dressing mix, 1 cup sliced pepperoncini peppers, and 1/4 cup pepperoncini brine. Cover and cook until the meat is very tender, 8 to 10 hours on the LOW setting or 4 to 5 hours on the HIGH setting.

Step 4

Transfer the roast to a clean cutting board. Shred with two forks into small pieces, or thinly slice across the grain. Reserve the sauce.

Step 5

When ready to serve, arrange a rack in the middle of the oven and heat the oven to 350°F. Split 8 hoagie rolls and place cut-side up on a baking sheet. Top each half with 2 slices provolone cheese. (Toast in 2 rounds or on 2 baking sheets if needed.)

Step 6

Bake until the cheese is melted, 5 to 7 minutes. Fill the toasted rolls with the beef and top with mild or spicy Giardiniera, as desired. Taste the sauce and season with more kosher salt and black pepper as needed. Spoon the sauce over the sandwiches and divide the rest into individual bowls or ramekins for dipping.