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Cut the potatoes as needed so they are in 2-bite pieces. Tiny potatoes won't need to be cut at all, larger ones can be quartered. The key is that the pieces are all uniform in size so they cook evenly.
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Put the potatoes in a medium saucepan and cover by 2 inches with water. Salt the water generously enough so that it tastes like the sea. Bring to a boil and cook until just tender, neither crunchy nor mushy. Don't be shy about spearing one out of the cooking water to slice into it and taste for doneness. Drain immediately.
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While the potatoes are boiling, cook the bacon using your favorite method until crispy.
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Make the dressing by whisking together the shallots, mustard, vinegar, oil, and water, until blended.
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Once the potatoes are cooked, combine them in a medium bowl with the cherry tomatoes and basil. Crumble the bacon into the salad. Drizzle 2 tablespoons of dressing over the potatoes and toss to coat. Taste and add salt and pepper as desired.
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To serve, set out 4 to 5 salad plates. Lay 2 leaves of lettuce on each plate and drizzle with a couple teaspoons of the dressing. Divide the potato salad amongst the plates. Drizzle on a little more dressing if needed.