Preheat the oven to 400°F.

Cut the ends from the squash, then slice in half lengthwise. Use a spoon to remove the seedy internal cavity from each squash half. Arrange the halves cut-side down on a parchment-lined baking sheet.

Roast the squash on middle rack of oven until it is fork-tender, 40-45 minutes. While the squash bakes, prepare the filling.

Set a large skillet over medium-high heat and add the olive oil. Once oil is shimmering, add the sausage and diced onion. Saute, breaking up the meat with a rubber spatula as it cooks, until it is browned and the onion is translucent, 6-7 minutes. Add the garlic and oregano and cook until fragrant, about 30 seconds.

Reduce the heat to medium-low and add the diced tomatoes. Season with salt and pepper. Cook, stirring occasionally, until the tomatoes begin to bubble and the liquid has reduced slightly, 2-3 minutes. Add the heavy cream and grated Parmesan cheese and stir. Continue cooking until the cream is gently bubbling, 1-2 minutes. Remove the skillet from the heat.

Remove the baking sheet from the oven and flip squash halves so they are cut-side up. Divide the sausage mixture evenly between each squash half, gently packing it into the center cavity. Divide the shredded mozzarella cheese evenly over each mound of filling.

Return the baking sheet to middle rack of oven and bake until the cheese is melted and lightly golden, 11-14 minutes.

Check to see that squash is done. Remove from oven or add time as needed.

Transfer the squash halves to serving plates and serve immediately.