Pierce the spaghetti squash with a knife and microwave on high for 8 to 12 minutes until tender, or roast in the oven. Let cool before handling.
Season chicken pieces with salt, pepper, and Italian seasoning. Melt 1 tablespoon of butter in a skillet over medium-high heat and cook chicken until no longer pink, about 6 to 8 minutes. Remove and set aside.
In the same skillet, add remaining butter, garlic, and shallot. Cook until softened. Stir in sun-dried tomatoes.
Pour in heavy cream and cook until bubbly. Stir in Parmesan cheese and baby spinach until combined.
Cut spaghetti squash in half lengthwise, remove seeds, and shred flesh into strands. Stir strands into the creamy mixture until well coated.
Garnish with fresh parsley if desired and serve hot.