Preheat oven to 400°F (200°C).
Slice the spaghetti squash in half lengthwise and scoop out the seeds.
Brush the interior of the squash with 1 tablespoon of olive oil and season with 1/2 teaspoon salt and 1/4 teaspoon pepper.
Place squash cut-side down on a parchment-lined baking sheet and roast for 40 minutes until tender.
While squash roasts, heat the remaining 1 tablespoon of olive oil in a large skillet over medium-high heat.
Season chicken cubes with remaining salt and pepper and sauté until golden brown and cooked through, approximately 8-10 minutes. Remove chicken from skillet and set aside.
In the same skillet, add minced garlic and sun-dried tomatoes, sautéing for 1 minute until fragrant.
Add baby spinach to the skillet and cook until just wilted.
Reduce heat to medium-low and stir in heavy cream, Parmesan cheese, oregano, and red pepper flakes. Simmer for 3 minutes until the sauce thickens slightly.
Use a fork to scrape the roasted spaghetti squash into strands and add them directly into the skillet.
Return the chicken to the skillet and toss all ingredients until thoroughly coated in the cream sauce. Serve immediately.