Preheat your oven to 350 degrees F. This initial step is crucial to ensure your casserole bakes evenly. While the oven is heating, coat an 8×10 or similar casserole dish with nonstick spray to prevent sticking.
Melt 2 tablespoons of the butter in a large skillet over medium-high heat. As the butter melts, it will create a beautiful base for your onions. Add the onion and cook until they begin to soften, about 5 minutes. You'll notice a sweet aroma filling your kitchen.
Next, add the yellow squash and 1 teaspoon of the salt. Stir frequently, allowing the squash to cook until it's just tender and starting to brown for about 10 minutes. The color change is a good indicator that they’re almost done.
Once your squash is ready, transfer the mixture to a colander set over a bowl or in the sink. This step is essential as it allows any excess liquid to drain, resulting in a firmer casserole. Let it drain for at least 5 minutes, gently shaking off as much liquid as possible.
In a large bowl, whisk together the eggs, Greek yogurt, milk, black pepper, thyme, cayenne pepper, and the remaining ½ teaspoon salt. This mixture will bring all the flavors together. You want a smooth consistency before adding the next ingredients.
Add the drained cheddar, Swiss, and squash mixture to the bowl. Gently stir to combine everything. Be cautious not to overmix, as you want to maintain some texture from the squash.
Transfer the combined mixture to the prepared baking dish. Spread it out evenly, ensuring that each bite contains a blend of all the ingredients.
In a medium microwave-safe bowl, melt the remaining 2 tablespoons of butter. Once melted, add the crushed crackers and stir until they’re evenly moistened. This topping will provide a delightful crunch!
Spoon the cracker mixture over the top of the casserole, ensuring it’s evenly distributed. This layer is what gives the casserole that classic, crispy topping.
Bake the Squash Casserole in the preheated oven until the filling is fully set at the edges and only slightly liquidy when you check the center with a knife, about 30 to 35 minutes. Once baked, let it rest for 10 minutes before serving. This waiting period allows the casserole to set properly and makes for easier serving.