Step 1

Place broccoli and water in a large microwavable bowl. Cover loosely with plastic wrap, and microwave on HIGH until tender, about 8 minutes. Set aside.

Step 2

Melt 3 tablespoons of the butter in a Dutch oven over medium-high. Add onion, and cook, stirring occasionally, until softened, about 5 minutes. Add garlic, and cook, stirring occasionally, 1 minute. Sprinkle flour evenly over onion mixture, and cook, stirring constantly, 1 minute. Whisk in milk, and cook, stirring constantly, until thickened, about 2 minutes. Reduce heat to medium, and whisk in mayonnaise, mustard, salt, and pepper until smooth. Add cheese, and stir until melted and smooth. Add broccoli, and stir to coat. Transfer to a lightly greased 13- x 9-inch broiler-proof baking dish, and cool to room temperature, about 30 minutes. Cover with aluminum foil, and chill until ready to bake, up to 1 day ahead.

Step 3

Preheat oven to 350°F. Remove casserole from refrigerator while oven preheats. Bake, covered, until hot and bubbly, about 1 hour.

Step 4

Place remaining 1 tablespoon butter in a medium-size microwavable bowl, and microwave on HIGH until melted, about 15 seconds. Add crackers and parsley, and stir to combine. Sprinkle evenly over casserole. Increase oven temperature to broil on HIGH, and broil casserole until top is golden brown, about 1 minute. Let stand 10 minutes before serving.