1. Heat oven to 350°F. For spice rub, combine paprika, black pepper, brown sugar, salt, cumin, oregano and cayenne in large bowl; whisk together until fully incorporated. Season pork cubes liberally with spice rub. Store extra spice rub in airtight container.
2. Combine seasoned pork cubes with milk and cola in large Dutch oven. Cover pan and bake at 350°F. for 2 1/2 hours until meat is very tender.
3. Allow pork to cool slightly; remove from pan and place in casserole. Use tongs to slightly crush pork cubes. Taste and adjust seasoning with additional spice rub if needed.
4. Heat panini sandwich press. Assemble sandwiches by spreading mayonnaise on the bottom half of each hoagie roll. Top with pork butt, ham, pickles and cheese. Spread mustard on top half of hoagie and close sandwich.
5. Spray panini grates with nonstick cooking spray. Grill sandwiches, top side down, until provolone has melted, about 5 minutes.