Preheat the oven to 350°F. Spray a 1½ to 2-quart baking dish with cooking spray.
In a large pan, heat the olive oil and 1 tablespoon of the butter over medium heat. When the butter is melted, add the yellow squash and onions, lightly season with salt and pepper, and sauté until they are crisp-tender, about 10 minutes. Note: To avoid a mushy casserole, be sure not to overcook the squash at this point. They will continue cooking in the oven.
Add the garlic and saute for another minute.
Remove from the heat and add the cheddar cheese, Parmesan cheese, sour cream, and half of the crushed crackers. Stir until well combined. Taste and adjust seasoning if needed.
Pour into the prepared baking dish.
Melt the remaining 2 tablespoons of butter and add to the remaining crushed crackers; stir to combine, making sure all of the cracker crumbs are coated in butter.
Sprinkle the butter/crushed cracker mixture over the top of the squash mixture.
Bake for 20 minutes or until the casserole is bubbly and the cracker topping is golden brown.