Prepare the dressing by mixing the Greek yogurt and mayonnaise in a bowl until smooth. Add the Carandini Bianca Sweet White Vinegar, lemon juice, and mustard, and mix well. Stir in the grated Parmigiano Reggiano and finely grated garlic, then season with salt and pepper until you achieve a smooth, creamy, slightly pourable consistency.
Season the chicken breasts with olive oil, salt, and pepper, then grill over medium-high heat until golden. Let them rest for a few minutes before slicing.
Cut the romaine lettuce hearts in half lengthwise and lightly brush them with some of the prepared dressing. Grill them cut-side down for 1–2 minutes, until lightly charred while still keeping a crisp texture.
Arrange the grilled lettuce on a serving plate, add the sliced chicken, and finish with croutons and Parmigiano Reggiano shavings. Drizzle with additional dressing just before serving.