Heat 1 TB olive oil in a heavy-bottomed pan over medium-high heat. When the oil is hot and begins to shimmer, sauté shallot and garlic slices for 1-2 minutes, until golden. Remove shallot and garlic from pan, and set aside.
If using campari or cherry small tomatoes, cut them all in half. If using larger tomatoes, core them and cut into quarters.
Add 1 more TB olive oil to the pan. Set tomatoes into the hot pan, and don't touch them for about 3 minutes, when the tomatoes have dark char marks. Toss and continue to blister the tomatoes for about 1 more minute. Remove tomatoes from the pan.
Add shallots, garlic, tomatoes, cucumbers, and anchovies to a blender basin. Remove the plastic lid insert from the blender lid to allow steam to escape, and cover with a towel. Blend until smooth. (Optionally, add all ingredients to a pot and use an immersion blender.)
Add vinegar to taste. (The amount needed will depend on the potency of your vinegar and your taste preferences.)
Next, add about 3/4 of the basil leaves and the cream, and blend until smooth. Taste, and add salt if needed.
Chill soup in the fridge for at least an hour before serving, and use within 3-4 days. Just before serving, roughly chop the remaining basil.
Serve soup chilled in 4 small bowls, or 2 large bowls, and top with basil.
Leftovers: Store leftovers in the fridge and use within 3-4 days.