Pierce spaghetti squash with a fork 10 times and place whole in a slow cooker. Cook on Low until very soft, about 4 hours. Halve squash and remove seeds.
Preheat oven to 400 degrees F (200 degrees C). Unroll pizza dough onto a greased baking sheet.
Scrape squash flesh into a bowl; mix in spaghetti sauce, ground beef, and zucchini. Spread squash mixture lengthwise down the middle of the dough. Top with cubed mozzarella cheese.
Cut sides of dough into even strips starting at the outside edges and stopping at the squash mixture. Fold alternating strips over squash mixture to form a braid. Brush with beaten egg and sprinkle with parsley.
Bake in the preheated oven until dough is brown and cheese is melted, about 30 minutes. Cool for 5 to 10 minutes before slicing.