"This is a technique that I’ve used for chicories for a long time because they’re bitter but have a lot of locked-in sugar content that comes out when you take them pretty far over ripping-hot heat. Then when you smoodge ’em with lemon juice and balsamic orsaba—and, of course, salt and pepper—it creates a whole new level of depth of flavor that’s true to life factual big time. Period."
Char the radicchio. In a large bowl, toss the radicchio with 2 tablespoons of the vinegar, 1 teaspoon of the salt, and half of the pepper. Let the mixture marinate while you heat a large heavy-bottomed sauté pan over high heat. Add 2 tablespoons of the oil.When the oil looks very hot (almost smoking), carefully add the radicchio to the pan so it sits in one layer. You may need to do this in batches. Cook on one side until charred and just starting to soften, 2 to 4 minutes. Transfer to a large bowl.
Put it together and serve. Add the remaining 1 tablespoon vinegar and 1 tablespoon of the lemon juice to the bowl. Toss and taste. It’ll be pretty bitter, but feel free to add more salt, lemon juice, or vinegar. Let the radicchio cool to room temperature.
Add the remaining ¼ cup oil, 1 tablespoon lemon juice, ½ teaspoon salt, and pepper plus the cherries to the bowl and give everything a good toss. Add the arugula and give it one more good toss. Using a peeler or rasp grater, peel or grate the cheese over the top of the salad and serve.
Note on balsamic vinegar: Bonus points for good balsamic, or saba if you can find it.
Note on cherries: This salad would also be good with sliced pear, apple, or peach, depending on what's in season.