Preheat grill to medium-high. Brush the grill grates with oil. Brush the chicken with the oil and sprinkle with the salt and pepper.
Grill the chicken, uncovered, for 3 minutes. Turn and top with 2 fontina slices each. Grill, covered, until the cheese is melted and the chicken is cooked through, about 3 minutes.
Stir the pesto and water. Place 1 cutlet each on 4 of the bread slices. Divide the prosciutto and drizzle the pesto mixture among the slices. Top with the remaining bread slices and serve.