Preheat the oven to 375°F and grease a 9x13-inch baking dish.
Bring a large pot of salted water to a boil and cook the spaghetti until al dente according to package instructions; drain and set aside.
In a large skillet over medium-high heat, melt the butter. Add the minced garlic and chopped green bell pepper and sauté until the pepper is tender, about 3–4 minutes.
Stir in the flour and Italian seasoning and cook for 1 minute to remove the raw flour taste.
Slowly whisk in the heavy cream, chicken broth, and milk. Bring to a simmer, stirring frequently, and cook until the sauce thickens slightly, about 2–4 minutes.
Remove the skillet from the heat and stir in ½ cup of the shredded mozzarella until melted. Season the sauce with salt and pepper to taste.
Add the drained spaghetti, shredded cooked chicken, and drained diced tomatoes to the skillet and toss until everything is evenly coated with the sauce.
Transfer the mixture to the prepared baking dish, spread into an even layer, and sprinkle the remaining mozzarella over the top.
Bake in the preheated oven for 15–20 minutes, until the edges are lightly browned and the cheese is bubbly. Let rest a few minutes before serving.