Begin by putting the oil, herbs and garlic in a heavy-bottomed pot over medium heat. Bring the oil up to 365 degrees F, then remove the herbs and garlic with a slotted spoon and drain on paper towels. They should be nice and crackly at this stage. Reserve for garnish.
Using a mandoline, cut the sweet potatoes into matchsticks. Put in a large bowl of ice water to remove any starch. Soak for a few minutes and rinse with fresh cold water until it runs clear. Drain the matchsticks and pat dry in a kitchen towel, to remove as much water as possible. Fry in 365 degree F oil, in small batches, until crispy and golden, 2 to 3 minutes. Transfer to paper cones, resting in cups, and season with Cajun spice mix. Peel the garlic cloves and sprinkle over the matchsticks along with the fried herbs before serving.