1. Cut the potatoes into 1/4-inch-thick slices. Place in a saucepan with enough water to cover. Bring to a boil over high heat. Cook until potatoes are tender, about 10 minutes. Drain.
2. Meanwhile, cook bacon in a small skillet over medium-high heat until crisp, about 8 minutes. Cool and crumble bacon; set aside. Cut tomatoes into 1/4-inch-thick slices.
3. Combine mustard, basil, salt, and pepper in a small bowl; mix well with a fork. Gradually beat in oil, then vinegar.
4. Arrange potato and tomato slices alternately on a serving platter. Drizzle dressing over top. Sprinkle with crumbled bacon.
VARIATION: For a pretty and flavorful idea, tuck a whole basil leaf next to each tomato slice in step 4.