For the Fondant Potato:

Cut the potatoes into barrel shapes, ensuring they are of the same size and shape (you should get 8 barrels).
Boil the potatoes for 6 minutes.
Heat olive oil in a pan and place the potato barrels in it. Sear them until they turn golden brown on both sides.
Add rosemary, smashed garlic, and butter. Cook for 1-2 minutes or until the butter melts.
Pour in the vegetable stock and add salt. Cook on medium-low heat until the potatoes are completely cooked, adding more stock if necessary.

For the Black Garlic Aioli:

In a food processor, add the egg, black garlic, salt, and lemon juice.
Start the food processor on medium speed and pour the vegetable oil in a thin stream. The mixture will thicken as you add the oil. Continue adding oil until it thickens to the point that it can hold soft peaks.

For the Glazed Carrots:

Boil the carrots in a deep, wide pan with 1 ½ cups of water. Season with salt and cook for 8-10 minutes or until the carrots are tender. Drain off any excess water.
Add the butter, brown sugar (or sweetener of choice), and salt to the pan. Stir to coat the carrots.
Cook for an additional 4-5 minutes, stirring occasionally, until a sauce forms.
Sprinkle the glazed carrots with chopped flat parsley.

For Assembling: