Warm the olive oil in a large pot over medium heat. Add the finely diced onion and minced garlic, then sauté for 3–4 minutes, until the onion becomes tender and the aromatics are fragrant.
Stir the tomato paste into the softened onion and garlic. Cook for approximately 1 minute while stirring continuously, allowing the paste to develop a deeper flavor and lose its raw taste.
Pour the chicken broth into the pot. Add the shredded rotisserie chicken, paprika, and dried Italian seasoning. Stir thoroughly so the chicken and seasonings are evenly distributed throughout the broth.
Add the drained, chopped sun-dried tomatoes and uncooked egg noodles. Increase the heat to medium-high and bring the soup to a simmer. Cook for about 10 minutes, or until the noodles are tender, stirring periodically to keep them from sticking.
Lower the heat to low. Gradually stir in the heavy cream, followed by the grated Parmesan and baby spinach. Continue cooking gently while stirring until the cheese has completely melted and the spinach has wilted.
Taste the soup and season with the salt and black pepper, adjusting the seasoning if needed. Ladle the hot soup into serving bowls and finish with red pepper flakes, if desired.