Place the basil, oil and garlic into a food processor and blend until smooth. Season, to taste, with sea salt and freshly ground black pepper.
Spoon the basil oil onto one side of the cut tomatoes.
Place the extra tbsp oil into a frying pan over a high heat.
Dredge the tomato slices in the flour, then place the tomatoes into the hot pan and fry for 2-3 minutes on each side, or until golden.