In a large bowl, combine the mushrooms, cannellini beans, onion, bread crumbs, ½ cup (15 grams) of parsley, 3 cloves of minced garlic, the dried rosemary, Worcestershire sauce, soy sauce, nutmeg, liquid smoke, salt, and pepper and mix well.
Roll the mushroom mixture into golf ball-sized balls.
Heat the canola oil in a large pot over medium-high heat until shimmering. Place the balls in the pot and cook for 1 minute on each side until browned all over, 3-4 minutes total.
Add the marinara sauce and stir to coat the balls.
Preheat the oven to 350°F (180°C).
Slice the rolls in half lengthwise. Place the bottom half on a 9x13-inch (23x33-cm) rimmed baking sheet. Place the meatballs on top, followed by any remaining marinara sauce in the pot, then the mozzarella. Top with the top half of the rolls.
Mix the melted butter in a small bowl with the remaining tablespoon of minced garlic, the Parmesan, and remaining teaspoon of parsley. Brush the tops of the rolls with the butter mixture.
Bake for 15 minutes, or until the bread is golden brown.