Place the quartered plum tomatoes in a large bowl along with the whole cherry tomatoes and use a stick blender to blitz them to a fine pulp.
Heat the olive in a large non-stick frying pan over a medium heat. Once hot, add the garlic and half the torn basil leaves. Cook for 30 seconds, then add the puréed tomatoes. Lower the heat and simmer the tomato sauce gently for 20 minutes, until the liquid has reduced by half and the sauce is syrupy. Check the seasoning, adding salt and pepper if needed.
Bring a large pan of salted water to a boil. Add the tagliarini and cook it for 1 minute less than the packet suggests. Remove the pasta from the water with a pair of tongs and place it in the tomato sauce, along with a ladleful of the pasta water.
Cook over a medium heat, stirring so the starch from the pasta thickens the sauce. Check the seasoning, then serve the pasta and sauce in warmed pasta bowls with the chopped burrata and the remaining basil sprinkled on top.
Finally, drizzle with a little extra olive oil and finish with a crack of black pepper.