Preheat the oven to 375°F. Lightly grease a 9×13 inch baking dish. Bring a large pot of salted water to a boil and cook the spaghetti until just shy of al dente. Reserve ½ cup pasta water, then drain.
In a large skillet over medium heat, melt the butter with the sun dried tomato oil. Add the diced onion and cook until softened, about 4 to 5 minutes. Stir in the garlic and cook for 30 seconds.
Add the sun dried tomatoes, tomato paste, and Dijon mustard. Cook for 1 minute to deepen the flavor.
Pour in the white wine and simmer for 2 to 3 minutes until slightly reduced.
Stir in the chicken broth and heavy cream. Bring to a gentle simmer and cook for 5 to 7 minutes until slightly thickened but still loose. The sauce should look thinner than you think it should. Stir in the lemon zest, red pepper flakes, 1 cup Parmesan, shredded chicken, and fresh herbs.
Add the drained spaghetti directly into the sauce and toss gently to coat. If needed, add a splash of reserved pasta water to keep it loose. Stir in 1 cup shredded mozzarella.
Transfer the mixture to the prepared baking dish. Sprinkle the remaining 1 cup mozzarella and ½ cup Parmesan evenly over the top.
Bake for 20 to 25 minutes until bubbly and lightly golden on top. Let rest for 10 to 15 minutes before serving so the sauce settles but stays creamy underneath.
