Whisk together vinegar, tarragon, mustard, honey, 4 tablespoons of the oil, 1⁄2 teaspoon of the salt, and 1⁄4 teaspoon  of the pepper in a small bowl.

Preheat oven to 400°F. Heat a cast-iron skillet over medium-high. Sprinkle 1⁄2 teaspoon of the salt and remaining 1⁄2 teaspoon pepper on all sides of the pork. Add 1 tablespoon of the oil to skillet; swirl to coat. Place pork in skillet, and cook, turning to brown on all sides, 3 to 4 minutes. Transfer to a rimmed baking sheet; place in preheated oven. Cook until a thermometer inserted in thickest portion registers 145°F, 10 to 15 minutes. Transfer to a cutting board; let rest 10 minutes.

Meanwhile, prepare farro according  to package directions. Drain; stir together farro and 2 tablespoons of the vinaigrette.

Heat remaining 1 tablespoon oil in cast-iron skillet over medium-high. Add Brussels sprouts, fennel, shallots, and remaining 1⁄4 teaspoon salt; cook, stirring, until wilted, 5 to 6 minutes. Add 2 tablespoons of the vinaigrette; toss to coat.

Slice pork. Divide farro, Brussels sprouts mixture, and pork evenly among 4 bowls. Top with apple; drizzle with remaining vinaigrette. Garnish with fennel fronds.