Preheat oven to 350 degrees F.
Cook the egg noodles according to the package directions for al dente, drain, rinse with cold water to stop the cooking process, drain again, and set aside.
Heat 1 tbsp olive oil in a large skillet over medium-high heat. Cook the chicken until no longer pink, stirring occasionally, about 5-7 minutes. Remove from the skillet and set aside.
Reduce the heat to medium, then add the remaining olive oil and butter to the pan. Cook the shallots for a couple of minutes, until softened, then add the garlic, red pepper flakes, and fresh thyme. Cook about a minute more, stirring constantly, until fragrant.
Stir in the flour and whisk for 2 minutes, then stir in the chicken broth, milk, sundried tomatoes, bouillon, salt, and pepper. Continue whisking until the sauce has thickened, about 4-5 minutes.
Add the chicken, noodles, and ¼ cup of the parmesan cheese. Stir until combined and pour the mixture into a greased 2-quart (or 9x13") casserole dish (I use EVOO spray). Top with the remaining ½ cup of parmesan cheese.
Bake for 30 minutes, uncovered, until bubbly. Garnish with freshly torn basil leaves before serving. Top with extra freshly grated parmesan, if desired.