Cut the ends off the spaghetti squash. Place it upright on a cutting board to create a steady base, then carefully slice it in half lengthwise. From there, scoop out the seeds.
Rub the insides of the spaghetti squash halves with olive oil and season evenly with salt and pepper. Place it cut-side down on a parchment-lined baking sheet and bake at 400°F for about 40-50 minutes, or until tender.
Remove the spaghetti squash from the oven and let it cool slightly. Use a fork to scrape the squash into strands and transfer them to a bowl. Set the empty squash shells aside.
While the squash bakes, make the Alfredo sauce. Heat the olive oil in a large skillet over medium-low heat. Sauté the shallot and garlic until softened and fragrant.
Reduce the heat to low, then add the milk and cream cheese. Whisk until the cream cheese is fully melted and smooth. Stir in the oregano, parsley, basil, salt, and pepper.
In a small bowl, whisk the cornstarch with one tablespoon of cold water. Slowly stir the slurry into the sauce and cook until thickened.
Once the sauce has thickened, stir in the grated Parmesan cheese, shredded rotisserie chicken, and spaghetti squash strands. Gently toss until everything is coated in the sauce.
Spoon the mixture back into the squash shells or serve it in a bowl. Serve warm and enjoy!