Cut the potatoes as needed so they are in 1 1/2-inch pieces. The key is that the pieces are all uniform in size so they cook evenly.
While the potatoes are boiling, cook the bacon using your favorite method until crispy.
In a small bowl make the dressing by whisking together the shallots, mustard, vinegar, oil, water, =1/4 teaspoon salt, and several grinds of black pepper.
Tear each lettuce leaf into 2 or 3 pieces. Pile into a medium bowl and lightly dress with some of the dressing. Transfer to 4 individual plates or one larger plate/platter.
Put the potatoes, cherry tomatoes, and basil into the same bowl you used to dress the lettuce. Crumble the bacon into the salad. Drizzle about 2 tablespoons of dressing over the potatoes and toss to coat. Taste and add more dressing, salt, or pepper, if needed.
Spoon the potato salad on top of the lettuce. Serve immediately.