Heat olive oil in a skillet until hot and shimmering. Toss in the yellow onion and green bell pepper, sautéing until they are soft and fragrant. The onions should turn translucent, which indicates they are ready. Avoid rushing this step as undercooked vegetables will detract from the dish's texture.
Stir in the cream of mushroom soup and cream of chicken soup, allowing them to blend smoothly with the veggies until you achieve a creamy consistency that coats the pan beautifully without sticking or scorching.
Gently mix in the cooked spaghetti pasta along with the shredded chicken and chicken broth. Ensure a nice, even distribution of ingredients so that everything feels homogenous. If the mixture appears too dry, adjust by adding more broth as needed.
Stir in the shredded cheddar jack cheese gradually, letting it melt and meld with the other ingredients. The dish should begin to emit a wonderful aroma. Sprinkling in the cheese gradually ensures an even melt and creamy texture.
Spoon the mixture into a greased casserole dish, smoothing it into an even layer. The mixture should look inviting and creamy, with colorful elements visible. Remember to scrape the skillet to include all those tasty bits for added flavor.
Place the casserole in a preheated oven and bake until it is bubbly and golden on top. The delightful smell will permeate your kitchen. If the top is browning too quickly, loosely cover it with foil during the final stages to retain moisture while it finishes baking.