Pierce the spaghetti squash several times with a fork to allow steam to escape, then microwave it for 8-12 minutes until the skin yields slightly to pressure. The squash will continue cooking with residual heat, so don't overcook it or it will become mushy. While the squash cooks, you'll have time to prep your other ingredients.
Pat the chicken dry with paper towels, then season generously on both sides with salt, freshly ground black pepper, and Italian seasoning. Heat 1 tablespoon of butter in a large skillet over medium-high heat until foaming, then add the chicken. Sear for about 7 minutes, turning once halfway through, until golden brown and cooked through (165°F internal temperature). The chicken doesn't need to be perfectly cooked at this stage since it will finish cooking in the sauce.
Remove the cooked chicken from the pan and set aside, loosely covered to keep warm. Add the remaining 1 tablespoon of butter to the same pan along with the minced garlic and diced shallot. Cook for 1-2 minutes, stirring frequently, until fragrant and the shallot begins to soften—this creates an aromatic foundation. Add the chopped sun-dried tomatoes and cook for another minute to allow their concentrated flavor to bloom. I like to use oil-packed sun-dried tomatoes because they add richness and don't need rehydration.
Pour the heavy cream into the pan with the aromatics and sun-dried tomatoes, stirring gently to combine. Bring to a simmer over medium heat for 1-2 minutes to allow the flavors to meld. Remove the pan from heat, then immediately stir in the freshly grated Parmesan cheese and fresh spinach, stirring until the cheese melts and the spinach wilts into the sauce. Add a pinch of red pepper flakes for a subtle warmth. Return the seared chicken and any accumulated juices to the pan, nestling it into the sauce to coat completely.
Cut the cooked spaghetti squash in half lengthwise and scoop out the seeds with a spoon. Using a fork, scrape the flesh lengthwise to create the characteristic spaghetti-like strands. I find that working from the center outward creates longer, more attractive strands. Add the squash strands directly to the cream sauce in the pan, gently tossing everything together until the squash is evenly coated and heated through.
Divide the creamy chicken and spaghetti squash mixture between serving plates or bowls. Top each portion with a generous sprinkle of fresh chopped parsley for color and a bright herbal note. Serve immediately while the dish is warm and the flavors are vibrant.