Preheat the oven to 200°C or prepare a barbecue.
Slice the tops off the beef tomatoes and scoop out the flesh and seeds into a saucepan.
Mix the shallot, lamb, breadcrumbs, mushrooms, and tarragon in a bowl and season well.
Fill the beef tomatoes with the lamb mixture, drizzle with oil, and replace the lids.
Bake in the oven or barbecue for 10 to 15 minutes until the meat is cooked through.
Combine the medium tomatoes, oil, and garlic with the reserved tomato flesh in the saucepan.
Season the sauce, bring to a boil, and simmer for 10 minutes.
Place the stuffed tomatoes on a platter and serve with the sauce drizzled around them.