Add the light mayonnaise, nonfat Greek yogurt, sun-dried tomatoes, garlic powder, onion powder, and Italian seasoning to a food processor or blender. Blend until smooth and creamy, scraping down the sides as needed.
Transfer the blended dressing to a large bowl. Stir in the shallot and grated Parmesan cheese.
Fold in the cooked chicken until evenly coated. Season with salt and black pepper to taste.
Refrigerate for 15–30 minutes to allow the flavors to fully develop.
Spoon the chicken salad onto the slices of bread. Top with spinach and the remaining bread slices.