Heat your oven to 350°F and grease a 9x13-inch baking dish with some cooking spray.
Melt butter in your big skillet on medium heat, then toss in the chopped cabbage and onion.
Cook the veggies for 12-15 minutes, stirring now and then, until the cabbage gets tender and golden.
Add salt and pepper to taste, then dump everything into your greased baking dish.
Mix the cream of chicken soup and mayo together in a bowl until it's nice and smooth.
Pour this creamy mix evenly over the cabbage, making sure you cover all the veggies.
Sprinkle the shredded cheddar cheese all over the top of the soup and cabbage mixture.
Mix the crushed Ritz crackers with melted butter in a bowl until they're all coated.
Sprinkle the buttery crackers over the cheese, covering the whole thing with an even layer.
Bake for 25-30 minutes until the top is golden brown and the cheese is melted and bubbly.
Take it out and let it sit for 5 minutes before serving so everything sets up.