Bring a large pot of salted water to a boil. Add the whole carrots (cut them in half if they don't fit in the pot) and cook until just cooked through, about 8 to 10 minutes. Drain and cut carrots into 1/2-inch thick slices.
Whisk together the lemon juice, garlic, cumin, cayenne, and salt in a large bowl. Slowly drizzle in the olive oil until emulsified and stir in the parsley. Add the cooked carrots and toss to combine. Serve cold or at room temperature.