Heat oven to 400°F. Line two rimmed baking sheets with aluminum foil. Spray lightly with nonstick cooking spray.
In a large bowl, combine all meatballs ingredients. Mix well, using damp hands to ensure mixture is incorporated.
Using a 1-inch cookie scoop, scoop meatballs onto lined baking sheets. Bake until meatballs are browned and edges are crispy, about 20 minutes (until internal temperature reaches 155°F). Recipe will make about 36 meatballs.
While meatballs bake, prepare the sauce. Over medium-low heat, melt butter in a large sauté pan or Dutch oven. Add onion, and sauté for 4 to 5 minutes until onions are translucent and softened. Add shredded carrot, and mix well. Add wine to deglaze the pan, and let come to a boil. Add pasta sauce, and reduce heat to low. Let simmer.
Transfer meatballs to a wire rack. Remove aluminum foil from baking pans, and replace with new aluminum foil. Arrange bottoms of pretzels rolls on pans. Top each pretzel roll half with 1 to 2 meatballs and equals amount tomato sauce and shredded Havarti.
Bake for 5 minutes in the oven until cheese melts. Place the other half of the pretzel roll on top, and bake an additional 5 minutes, until buns are lightly toasted. Serve immediately.