Combine garlic, lemon juice, balsamic, lime juice, syrup, paprika, salt, and pepper in a medium bowl. Slowly add olive oil while whisking. Gently fold in cheese, careful not to break it up too much. Taste and add more salt if needed. Refrigerate until ready to use.

Heat a grill or grill pan to medium-high.

If chicken breast are thick, slice them in half horizontally so you have 4 pieces of chicken breast. Drizzle chicken with half of the vegetable oil and rub the grill or grill pan grates with remaining half of the oil. Generously season chicken with salt and pepper. Grill chicken until cooked through, about 5-6 minutes a side. Remove to a plate. Once cool enough to handle, slice into strips.

Heat a large frying pan over medium heat. Add bacon in a single layer and cook until crisp and brown on both sides. Remove to a paper towel-lined plate, keeping pan over the heat. Once bacon is cool enough to handle tear into pieces.

Add tortilla strips to the pan and cook, stirring frequently, until crisp and crunchy, about 5 minutes. Remove them to a separate paper towel-lined plate and sprinkle with salt.

Arrange romaine lettuce on a large platter or divide between 4 large plates. Top with arugula, tomatoes, eggs, chicken, bacon, tortilla strips, corn, peaches, and avocado. Drizzle dressing over the top and serve.