Step 1Boil the water in a 3-quart saucepan. Add the salt and stir in the farro. Return to a boil, then reduce the heat and simmer over medium-low heat until the farro is tender, about 30 minutes. Drain.
Step 2While the farro is cooking, grill the radicchio. Cut each head of radicchio into 6 wedges. Brush the wedges with 3 tablespoons olive oil. Grill over medium high heat on a cast-iron grill pan or outdoor grill until the radicchio is charred and tender, 10 to 12 minutes.
Step 3Remove the radicchio from the grill and let it cool enough to handle. Remove the core from the radicchio wedges. Discard the core; cut the remaining radicchio into 1 1/2-inch pieces. Add to the farro and toss.
Step 4Using a mortar and pestle, grind the anchovies to a paste. Add the garlic and crush it with the anchovy. Add the balsamic vinegar, lemon juice, and remaining 2 tablespoons olive oil and mix.
Step 5Pour the dressing over the farro and toss. Stir in the capers and prosciutto.
Step 6Spoon into a serving bowl and sprinkle with chopped parsley.