Preheat oven to 400 degrees and lightly grease a 9x13 pan. Cook the egg noodles according to the package directions. Drain and pour pasta to prepared pan.
Meanwhile, melt butter in a medium-sized saucepan over medium heat. Add in onion and saute 5 to 7 minutes, until softened. Stir in garlic and flour and cook 1 minute. Slowly pour in chicken broth and milk, season with salt and pepper, and bring to a simmer, stirring constantly.
Once mixture has thickened, stir in peas, cheddar cheese, and chicken. Turn off the heat and stir until cheese has melted. Pour over pasta in the 9x13 pan.
In a small bowl, use a fork to mix together crushed crackers, parmesan, and olive oil. Sprinkle over the pasta.
Bake in the preheated oven, uncovered, for 15 to 20 minutes, until crackers are lightly browned. Serve hot.