Preheat the oven to 200C/400F/Gas 6 or prepare a barbecue.
Slice the tops off the beef tomatoes, reserving the tops to use as lids later. Scoop out the flesh and seeds from the centre and place into a saucepan.
Mix the shallot, mince, breadcrumbs, mushrooms and tarragon in a bowl. Season with salt and freshly ground black pepper.
Stuff the tomatoes with the mince mixture (do not overfill as the mixture will expand when cooking and could split the skin), drizzle with oil and place the lids on top.
Place the stuffed tomatoes onto a barbecue for 10-15 minutes, or until the mince is fully cooked. Alternatively bake in the oven for the same time.
To make the sauce, add the tomatoes to the saucepan containing the flesh from the beef tomatoes, then add the oil and garlic. Season with salt and pepper and bring to the boil. Simmer for 10 minutes.
To serve, place the stuffed tomatoes onto a large serving platter and drizzle around the sauce.