Warm a drizzle of olive oil in a medium-sized skillet set over medium heat. Add the thinly sliced onion along with a pinch of kosher salt. Cook slowly, stirring occasionally, until the onion becomes deeply golden and caramelized, about 30 minutes.

While the onion cooks, preheat your oven to 400°F (200°C). Spread the cubed butternut squash on a baking sheet, drizzle lightly with olive oil, and season with salt and pepper. Roast in the oven for 15 minutes or until the squash is fork-tender. Remove from the oven and set aside.

Once the onions are fully caramelized, stir in the broccolini and sliced cremini mushrooms. Sauté for 5 to 10 minutes until the vegetables are tender yet vibrant. Scatter the minced garlic over the mixture and cook briefly until aromatic, ensuring not to brown the garlic.

Lightly dust your work surface with flour and roll out the pizza dough into a large circle about 1/8 inch thick. Place the dough onto a sheet of parchment paper for easier handling.

Spoon the marinara sauce over one half of the dough, spreading it evenly but leaving a border around the edges. Layer the broccolini and mushroom mixture on top of the sauce. Add the roasted butternut squash, distributing it evenly. Finally, arrange slices of mozzarella or sprinkle the shredded mozzarella over the filling.

Fold the dough over the filling to create a half-moon shape, pressing the edges together firmly to seal. Crimp or twist the edges for a decorative finish if desired. Carefully transfer the parchment with the calzone onto a baking sheet.

Using a sharp knife, cut a small slit into the top of the calzone to allow steam to escape while baking. Place it in the preheated oven and bake for 15 to 20 minutes, or until the crust is puffed, golden, and crisp. Remove from the oven and let rest briefly before slicing and serving.