Heat a large pot of water until it reaches a rolling boil, then add the broccoli florets and cook for 2 minutes. Watch for the florets to turn bright green while still feeling firm at the center.

Drain the broccoli very well in a colander and set it aside while you prepare the creamy mixture. Let steam escape and shake away as much water as possible so the finished casserole stays thick.

Whisk the mushroom soup, mayonnaise, eggs, dried minced onion, and freshly grated cheddar in a large mixing bowl until evenly combined. The sauce should look smooth and creamy, with no visible streaks of egg or pockets of unmixed cheese.

Add the drained broccoli to the bowl and fold until every floret is coated, then transfer the mixture to a greased 2 qt casserole dish or 8-inch dish. Spread the broccoli into an even layer so the center and edges bake at the same pace.

Scatter the crushed cheese crackers evenly over the top and bake uncovered at 400°F for 40 to 45 minutes. The casserole is ready when the edges actively bubble and the cracker crust is deep golden brown.