For the salad: 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; crumble and set aside.

Place chopped lettuce in a large glass dish or bowl; top with a layer of red onion, peas, shredded cheese, cauliflower, and bacon.

For the dressing: Whisk mayonnaise, Parmesan cheese, and sugar together in a bowl until smooth. Drizzle over salad and refrigerate until chilled.