For the tomato oil: in a blender at low speed, mix the tomato paste and the vegetable oil. Run until the oil turns bright red, and the blender hopper is warm to the touch (10-15 minutes). Drain the oil through a strainer, and then hang it in a coffee filter.
For the tomatoes: take a hand-held propane torch. On a fireproof surface (like a sheet pan on a stove top) blister the tomato skin with the torch’s flame. When the tomato is black all over, run the skins off with a clean towel. If torch is not available, blanch tomatoes and peel off skins.
To complete the salad: cut the tomatoes into attractive shapes (exactly how will depend on which tomatoes you used - get creative). In a bowl, toss them in a little oil, a little vinegar, some sea salt, and some cracked pepper to taste. Arrange them decoratively on a plate, and drizzle a little more dressing from the bowl around them. Add a twist of pepper, garnish with the little basil leaves, and you’re done!
If you want to dress it up a little bit, you can add some croutons, mozzarella cheese, balsamic vinegar, parmesan, or whatever else you want, but all you really need are great tomatoes, simple dressing, salt, and pepper.