Fill a pot halfway with water, add 1 teaspoon salt and bring to a boil over medium-high heat. Add the carrots and cook until just softened, 3 to 5 minutes.
Transfer carrots to a bowl of ice water until cooled, about 2 minutes. Remove carrots from ice bath and pat dry.
Preheat a grill pan over medium-high heat. Brush carrots with olive oil and sprinkle with pepper. Place carrots on the grill and cook until well marked, 3 to 4 minutes per side. Transfer to a serving plate.
Place queso fresco on the grill and cook for 30 seconds per side. Rough chop queso fresco and toss with parsley.
Sprinkle the carrots with the queso fresco and parsley mixture.