Place the bread and 1 tablespoon of the oil in a bowl and toss together. Transfer to a baking sheet and cook under a preheated hot grill, turning once, until golden and crisp. Set aside.
Mix together another tablespoon of the oil and the cumin and season well, then rub over the chicken breasts. Heat a griddle pan until smoking hot, add the chicken and cook for 12–15 minutes, turning frequently, until charred and just cooked through. Leave to cool slightly, then cut into slices.
Make the dressing. Place the garlic, Parmesan, soured cream and mayonnaise in a mini food processor or blender and whizz until smooth, then add lime juice and salt and pepper to taste.
Arrange the lettuce, croutons and chicken on serving plates. Drizzle over the dressing and sprinkle with the red chilli to serve.