In a medium saucepan, bring the water, 1 tablespoon of the oil, and ½ teaspoon of the salt to a boil over high heat. Stir in the farro and reduce the heat to medium low. Cover and cook until the farro is tender and the liquid is mostly absorbed, 20 to 25 minutes. Remove the pan from the heat and let the farro cool uncovered.
Meanwhile, make the Asiago crisps. Heat the oven to 375ºF. Line a baking sheet with parchment paper. For each crisp, place 1 tablespoon of cheese on the prepared baking sheet, leaving about 3 inches between each mound (you should have eight mounds total). Spread each mound to a circle 3 inches in diameter. Bake until the cheese melts and just begins to brown, 4 to 6 minutes. Remove the cheese from the oven and let it cool on the sheet (the rounds will crisp upon cooling).
Put the hazelnuts on another baking sheet and toast them in the oven with the Asiago cheese for about 6 minutes, shaking the pan once or twice.
Pour the vinegar into a large bowl. Slowly whisk in the remaining 5 tablespoons of oil until incorporated and thickened. Whisk in the honey, shallots, parsley, pepper, and remaining ½ teaspoon of salt.
Add the apple to the bowl, toss to coat all the pieces, and then remove them with a slotted spoon, leaving as much dressing in the bowl as possible. Set the apple aside.
Add the lettuces to the bowl and toss to coat. Divide the lettuces among four plates and top evenly with the chicken, cooled farro, dressed apple pieces, toasted hazelnuts, and Asiago crisps.
Tip: Try using leftover roast turkey instead of rotisserie chicken, pears instead of apples, and Parmesan instead of Asiago cheese.