Slice the yellow squash into 1/2-inch rounds and set aside. Finely dice the onion into 1/4-inch pieces and mince the garlic, keeping them separate. Crush the butter crackers roughly by hand until you have a combination of fine crumbs and small pieces—this creates better texture than uniform crumbs. Having everything prepped and ready makes the cooking process smooth and prevents overcooking any components.
Bring a large pot of salted water to a boil and add the sliced squash. Boil for exactly 3 minutes—this softens the squash just enough so it will meld into the casserole without becoming mushy. Drain in a colander and rinse with cold water to stop the cooking process and remove excess starch. Set aside to drain thoroughly.
Heat a large skillet over medium-high heat and add the ground beef, breaking it into small pieces as it cooks. Once the beef is mostly browned, add the diced onion and minced garlic, stirring frequently until the onion is softened and translucent, about 3-4 minutes. This builds flavor by allowing the aromatics to cook directly in the meat's fat. Don't drain the fat—it carries flavor into the casserole.
In a large bowl, combine the cream of mushroom soup, canned tomatoes with green chilies, and 1 cup of the cheddar cheese. Beat the eggs in a separate bowl until smooth, then add them to the mixture, stirring constantly to ensure they incorporate evenly and don't scramble. Add the cooked beef mixture from Step 3 and stir until fully combined. Finally, gently fold in the drained squash from Step 2 along with the black pepper, being careful not to break up the squash pieces too much.
Preheat your oven to 350°F. Transfer the casserole mixture from Step 4 into a 9x13-inch baking dish, spreading it evenly. Sprinkle the crushed crackers evenly over the top, then scatter the remaining 1/2 cup of cheddar cheese over the crackers. I like to top the cheese last so it melts beautifully and creates a golden crust without the crackers burning underneath. Bake for 20-30 minutes until the cheese is bubbly and the top is golden brown.
Remove the casserole from the oven and let it rest for 10 minutes before serving. This resting period allows the eggs to set fully, giving the casserole a better structure so it holds together when plated rather than falling apart. The flavors also meld and settle during this time, making each bite more cohesive.