Preheat oven to 350 F. Cook pasta according to package directions, drain and place into a large bowl. In a large saucepan over medium heat, melt butter, cook minced garlic until fragrant. Add in flour and cook for a minute to brown.
Pour in milk and chicken broth. Season with salt, pepper and dried oregano. Add in 1 cup shredded cheddar cheese. Continue to cook over medium heat, while whisking constantly until smooth and thickened.
Mix the spaghetti with the cooked and diced chicken and the cheese sauce. Spread the mixture out into a large greased baking dish. Sprinkle shredded cheddar cheese on top and bake for 25-30 minutes.