Preheat the oven to 375 degrees. Pierce the sweet potatoes a couple of times with a fork and roast on a small baking sheet until soft, about 50 minutes.
Smash the garlic cloves and sprinkle with a pinch of salt. Using the flat side of a large knife, mash the mixture into a coarse paste. Add to the mayonnaise along with about 2 tablespoons water. Gradually whisk in the olive oil and season with pepper.
Halve each sweet potato lengthwise, sprinkle with salt and pepper and top with the aeoli.