Preheat the oven to 375°F and grease a 9×13-inch baking dish; set aside.
Bring a large pot of salted water to a boil and cook the 10 ounces of spaghetti until al dente according to package directions; drain and set aside.
In a large skillet over medium-high heat, melt 2 tablespoons unsalted butter, then sauté the minced garlic and chopped green bell pepper until the pepper is tender, about 3–4 minutes.
Sprinkle in ¼ cup all-purpose flour and 1 teaspoon Italian seasoning, stirring constantly and cooking for about 1 minute to remove the raw flour taste.
Slowly whisk in ¼ cup heavy whipping cream, ½ cup chicken broth, and ½ cup milk; bring to a simmer and cook, stirring frequently, until the sauce thickens slightly.
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, 2 cups shredded cooked chicken, and the drained 14-ounce can of diced tomatoes to the skillet and toss gently until everything is evenly coated.
Transfer the mixture to the prepared baking dish, sprinkle the remaining 1 cup of shredded mozzarella evenly over the top, and spread into an even layer.
Bake in the preheated oven for 15–20 minutes, until the cheese is melted and bubbly and the edges are lightly browned; let rest a few minutes before serving.