Wash the spaghetti squash, then pierce the squash all over with the tip of a sharp knife (This will allow the squash to release steam/pressure in the microwave, so don't skip this step).
Place the squash in the microwave and cook on high for 5 mins, then rotate the squash. Repeat this step of cooking for 5 mins and rotating until you have reached 15 mins of total cook time. Allow the squash to cool for 10-15 mins.
While squash is cooling, preheat oven to 375 degrees.
In a large oven-safe skillet (I use cast iron) melt 3 tbsp butter over medium-high heat. Season chicken with salt and pepper and cook for 6-7 minutes, tossing occasionally to make sure all sides are browned. Use a slotted spoon or tongs to remove the chicken from the skillet and set aside on a plate.
Melt the last 1 tbsp of butter into the same skillet and stir in garlic until fragrant.
Stir in the heavy cream, cream cheese, and parmesan cheese until smooth and simmer until thickened, for 3-4 minutes. Season with extra salt and pepper to taste if needed.
By this time, your spaghetti squash should be done cooling. Cut the squash in half lengthwise and scoop out the seeds. Use a fork to scrape the sides of the squash into spaghetti-like strand. (If your squash doesn't shred easily, place it on a microwave safe plate face down and microwave for an additional 2-5 mins.)
Add the shredded squash and chicken into the skillet and toss everything together.
Top with shredded mozzarella and bake uncovered for 15-20 minutes until sauce is bubbling and cheese is melted.
Garnish with chopped parsley and serve warm. Store leftovers in fridge for up to 5 days.
This recipe yields about 7 cups, depending on the exact size of your spaghetti squash. Each serving is approximately 1 cup.