Note: Be sure to start the beef the day before you plan to make the sandwiches.
- Make the beef: Season beef with salt, pepper, italian seasoning, and fennel seed. Set aside at room temperature for 2 hours.
- Preheat a grill to 275 degrees. Transfer beef to grill and cook until internal temperature reaches 120 degrees, about 1½ hours. Remove beef from heat and set aside at room temperature to rest for 1 hour, then refrigerate overnight.
- Make the beef dip: Combine all ingredients in a 4-quart saucepan. Bring to a boil, then set aside and keep warm.
- Assemble the sandwiches: Slice beef as thinly as possible. Transfer meat into beef dip, then divide evenly among sandwich rolls. Dip entire sandwich into beef dip until bread is saturated. Transfer sandwiches to plates and garnish with giardiniera.