Preheat your oven to 180℃
Place all of the vine tomatoes in a baking tray along with the 3 whole cloves of garlic with the skins on. Season well with a good pinch of salt and a generous glug of olive oil, make sure everything is coated well and place in the oven for 40mins to roast.
When the tomatoes have 20mins of cooking left, in a large heavy bottomed saucepan fry the shallots in a little oil on a medium heat until softened - this will take around 5mins. Add in the grated carrot, leeks and bay leaves and cook for a further 5mins, add in the crushed garlic and cook for another 3mins until everything is smelling fragrant.
Once the veggies have softened and reduced, add in the tomato paste and cook off for 5mins, followed by the dried oregano.
Add in the smoked pancetta and cook into the veggies for 6mins then add in the mince meat and chunks of lamb shoulder. Cook until all of the meat is browned, at this stage you may feel the bottom of the pan is feeling slightly dry - this is perfect! Pour in the wine to deglaze, this will help loosen the bits sticking to the bottom (you want these because its all flavour!)
Your tomatoes should be roasted by now, some will have blistered and burst and the garlic should be lovely and soft. Take the tomatoes off the vines and squeeze the garlic out of their skins and pour everything into the saucepan - juices and all! Stir well so everything is combined then add in the lamb stock and balsamic vinegar, season to taste with salt and pepper (If you feel you need to alter any seasoning, this is the time to do it)
Bring everything to a rolling simmer then clamp a lid on and place on the lowest heat; allow to cook for 3 hours, stirring every hour to make sure the bottom doesn't catch. After 2 hours, take the lid off and allow to cook for the last hour without the lid to help the sauce reduce and thicken. At this stage, pour in 2 tbsps of olive oil, this will help make the sauce lovely and glossy. Check the chunks of shoulder, you will know the ragu is ready when you are able to easily squash them with the back of a spoon, if not continue to cook for another 30mins then check again.
When you think your ragu us ready, turn off the heat and let rest whilst you cook the pasta; set a saucepan of salted water on a high heat and bring to the boil. Cook your pasta until al dente then with a pair of pincers carefully pick up the pasta and transfer straight into the ragu dragging the drops of pasta water with it, this will help loosen the sauce. Stir well to ensure all of the pasta is coated in the sauce, serve immediately in shallow bowls. Grate a generous amount of pecorino over everything and garnish with some basil leaves. Finish with a little drizzle of extra virgin olive oil, or truffle if you're feeling fancy!