Bring a saucepan of lightly salted water to a boil and cook the whole cauliflower until tender, about 10 minutes. Drain well and break into small florets.
Have a bowl of water handy to keep your hands wet while making meatballs. Meatballs are formed by flattening a lemon-sized portion of meat into a thin patty and wrapping the patty around a cauliflower floret to completely enclose. Form into an oval shape, then dip into the eggs and dredge in flour, tapping off any excess flour.
Cook the meatballs in oil until golden, about 4 minutes, without crowding the fryer. Remove with a slotted spoon to paper toweling to drain.
For the sauce:
Heat the extra-virgin olive oil over medium-high heat in a large saucepan. Dissolve the tomato paste in the water, and add to the pan along with harisa and ground red chili. Add the meatballs and cook covered until most of the liquid evaporates, about 25 minutes. Add a little water to rehydrate sauce if it is dries out before that time. Serve meatballs covered with sauce.