Bring a large pot of lightly salted water to a boil and cook carrots until softened slightly yet firm to the bite, 5 to 10 minutes. Make sure not to overcook because they continue cooking even after they have been taken off the stove. Drain and cut into 1-inch long strips.
Stir together olive oil, balsamic vinegar, oregano, salt, and cayenne pepper in a small bowl. Add garlic to marinade and mix to combine. Place carrot strips into a container with a tight-fitting lid and pour marinade on top. Cover and marinate in the refrigerator for 24 hours.
