Quarter the cucumber lengthwise and trim off the triangular wedge of seeds. Cut the cucumber into a very small, even dice. Transfer it to a mixing bowl.In a food processor, combine the garlic, vinegar, shallots and dill. Pulse until finely chopped but not pureed. Add the mixture to the cucumbers; add the yogurt. Fold together with a rubber spatula, adding the olive oil and lemon juice. Season liberally with kosher salt and pepper, starting off with 1 tablespoon salt. Taste for seasoning. You can store Tsatziki in a covered, clean jar in the refrigerator for up to 1 week.