Heat the olive oil in a large skillet over medium-high heat.
Add the onions and cook for 3 to 4 minutes.
Add the garlic and all of the seasonings. Cook for another minute or until fragrant.
Add the mixed vegetables, chicken, and the broth, reserving ½ cup.
Bring the sauce to a simmer and cook over medium heat for five minutes.
While the sauce is simmering, add the flour and reserved broth to a small bowl and whisk until smooth.
Pour the flour/broth mixture into the pan and stir. Simmer for 3 to 4 minutes to thicken, stirring frequently.
Turn the heat down to low, stir in the hot sauce and sprinkle in the Parmesan cheese, 1 tablespoon at a time. Completely work the Parmesan cheese in before adding more. Adding all of the Parmesan at once may result in it getting "gummy" and clumping up rather than melting into the sauce.
Taste and adjust the salt, pepper, and hot sauce to your liking.
You can either serve the sauce over the egg noodles or mix it all together.
Garnish with minced Italian parsley, if desired.