1. Toss shallot slices to separate them into rings. Have ready a slotted spoon and a double layer of paper towels. Heat oil to 275° in a small, deep heavy saucepan and drop in shallot rings.
2. Cook shallots, stirring often, until they turn a uniform light brown--this will take about 8 to 12 minutes. Turn off the heat when they look almost done so they don't burn. Lift shallots from oil with slotted spoon and drain on paper towels. Reserve 2 tsp. shallot oil for vinaigrette and let cool. Save the rest for stir fries and any salad dressings.
3. Make vinaigrette: Whisk vinegars, sugar, lemon juice, 1/4 tsp. salt, and 1/2 tsp. pepper together in a large bowl until salt and sugar dissolve. Add reserved shallot oil and the minced shallots and whisk well to blend. Season to taste with more salt, pepper, and lemon juice.
4. Slice cucumbers into 1/4-in. slices with a knife or on a mandoline. Toss cucumbers and tomatoes with vinaigrette. Add mint, Thai basil, and shiso if using.
5. Arrange salad on a platter and top with pickled leeks and fried shallots.
Make ahead: Fried shallots, up to 2 days, stored airtight at room temperature.
*Thai basil has narrow leaves, a purplish stem, and an anisey scent. Shiso, a beautiful notch-edged red or green herb, lends delicious fragrance to a dish (it's often served with sushi); the red is more pungent. Vietnamese pickled leeks are crunchy and mildly spicy-sweet. Find all at Asian markets.