Preheat the oven to 375 degrees F. Bring a medium saucepan of salted water to a boil. Add the farro and cook until just tender, about 25 minutes; drain and set aside.
Meanwhile, season the pork with 1/2 teaspoon salt and a few grinds of pepper. Combine the lemon juice, 1 teaspoon mustard and the garlic in a small bowl; brush all over the pork. Heat 1 tablespoon olive oil in a large ovenproof skillet over medium-high heat. Add the pork and cook, turning, until browned on all sides, about 5 minutes. Scatter the artichokes around the pork and transfer the skillet to the oven. Roast until a thermometer inserted into the center registers 145 degrees F, about 15 minutes. Transfer the pork to a cutting board; let rest 5 minutes.
Whisk the vinegar and the remaining 1 tablespoon olive oil and 1 teaspoon mustard in a medium bowl. Add the farro, pecorino, scallions, mint, 1/4 teaspoon salt and a few grinds of pepper; stir to combine. Slice the pork. Serve with the artichokes and farro salad.