Heat a skillet over medium heat; pour sesame seeds into the hot skillet. Cook, stirring often, until sesame seeds are lightly browned and fragrant, 3 to 5 minutes. Remove from heat.

Mix carrots, apple, toasted sesame seeds, and parsley together in a bowl.

Whisk lemon juice, vinegar, sugar, garlic, salt, and pepper together in a separate bowl; slowly drizzle safflower oil into lemon juice mixture while continuing to whisk. Pour dressing over carrot mixture; toss to coat.