Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels. Chop into small pieces.
Layer iceberg lettuce, cauliflower, red onion, bacon, mayonnaise, sugar, and Parmesan cheese in a large bowl, in that order. Cover tightly with plastic wrap. Place a heavy pan on top of the salad to press it down.
Refrigerate for 24 to 36 hours, checking occasionally that salad is still pressed down.