Make salad: Combine 1 qt. water, the farro, and 1 1/2 tsp. salt in a 3- to 4-qt. saucepan. Bring to a boil over high heat, then cover, reduce heat to low, and simmer until farro is tender, 25 to 30 minutes. Drain farro and spread on a baking sheet to cool and dry at least 5 minutes. Transfer to a serving bowl, add parsley and thyme, and toss to combine.
Make dressing: In a small bowl, whisk together lemon juice, honey, shallot, and salt. Whisk in oil in a thin stream. Pour over farro mixture and toss well to coat.
Pat halloumi dry. Set a 12-in. frying pan (not nonstick) over medium-high heat. Add 1 tbsp. oil, heat for a minute, then add halloumi in a single layer. Cook, turning once, until golden brown, 1 1/2 to 4 minutes total. Transfer cheese to a work surface and cut into 1/2- to 3/4-in. pieces.
Wipe out frying pan with a paper towel, then add remaining 2 tbsp. oil and return to medium-high heat. Add apples and remaining 1/4 tsp. salt. Cook, stirring, 2 minutes. Add sugar and cook, turning apples occasionally, until golden and tender, 5 to 9 minutes.
Transfer apples to work surface and cut in half crosswise. Toss apples and halloumi with farro mixture. Serve warm or at room temperature.
*Find farro, a type of wheat berry, at well-stocked grocery stores. Most farro sold today is semipearled, a process that removes some of the bran for quicker cooking. If the package instructions call for soaking overnight, you have whole-grain farro and will also need to cook it longer--usually 45 minutes to an hour.