Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper or place a wire rack on the sheet.
Place the garlic croutons in a food processor or blender and pulse until they become fine crumbs.
In a shallow bowl, whisk together the creamy Caesar dressing and the zesty Italian dressing until combined; set aside.
In another shallow bowl, mix the shredded (or grated) Parmesan cheese with the crouton crumbs until evenly combined.
Working with one chicken breast at a time, dredge it in the dressing mixture to coat both sides, then press it into the Parmesan–crouton mixture so the crust adheres evenly.
Place the coated chicken breasts on the prepared baking sheet or on the wire rack set over the baking sheet, leaving space between pieces.
Bake for 30–40 minutes, or until the chicken is cooked through and juices run clear (internal temperature 165°F / 74°C).