Cut onion and shallots into thin slices. Peel off carrots, divide into 3 logs. Cut each log into 0.18''/4.5 mm thick slices. Cut into batonnet, and dice. For the tomatoes, wash them, slice off ends, and cut flesh around the core of the tomatoes. (Fresh tomatoes can be substituted for 10oz/300g drained canned diced tomatoes). Save core (pulp) for your next salad. Dice out tomato flesh; set aside. In a large and hot skillet, add butter and olive oil – cook onions, shallots, and carrots for 8 min of medium heat. Season with salt and ground black pepper. Add tomatoes along with thinly chopped rosemary, thyme, and basil to taste. Cook for 5 minutes more. Readjust seasoning if needed.
Line baking tray with a silicone mat, and spread out salt evenly. (The salt can be reused afterward). Using salt in baking diffuses heat evenly and prevents from drying out. Clean potatoes, and remove eyes. With the tip of your pairing knife, draw an oval shape on the surface of the potato, and make a clean cut. Use a melon baller to scrap out more flesh; do not dig in too much though. Save potato scraps for your next soup. Season potato cavities with salt, pepper, and some olive oil. Stuff each potato generously. You may have enough stuffing to make a couple of extra potatoes.
Set temperature to 325ºF/160ºC. Bake stuffed potatoes for 2 hours; or until cooked through. Tent with aluminum foil if it gets too much color during baking. Remove from oven, let cool 10 minutes before serving. Brush stuffed potatoes with olive oil and garnish with chopped basil – Bon appétit!