Make the croutons: Heat oven to 400°F (200°C). Spread bread cubes over a baking sheet and toss with salt, pepper, a pinch of paprika, and 2 tablespoons of olive oil. Bake for 8-10 mins, turning the croutons a few times during cooking so they brown evenly.
Heat the chicken (optional): Heat a skillet over medium-high heat. Once hot, add the remaining tablespoon of olive oil. Place the precooked shredded chicken in the skillet in a single layer. Sear the chicken and warm it up for about 90 seconds on each side or until it’s brown outside. Remove from heat and set aside.
Assemble the salad: Prepare a large mixing bowl. Add romaine lettuce, red onion rings, ⅔ shredded chicken, ⅔ croutons, and most of the dressing. Mix well. Scatter the rest of the chicken and croutons and drizzle with the remaining dressing. Spread the parmesan on top and serve right away.