Make the Vinaigrette:

1. Add all the vinaigrette ingredients except the olive oil to a blender and blend for 30 seconds or so on low speed to combine.
2. With the blender running on medium speed, pour in the oil in a slow steady stream.
3. Taste and adjust the amount of salt and pepper if necessary. Pour into a covered container or squeeze bottle, and refrigerate until ready to use. Shake well before using.

Make the salad:

1. Make some croutons
2. Fill a large dutch oven or stock pot with water and a couple tablespoons of salt, and bring to a boil.  Add the potatoes and let simmer until they are tender when poked with a fork, about 15 minutes.
3. Pour the the potatoes into a colander to drain and then transfer them to a medium sized bowl and toss with vermouth (if using) and about 1 tsp each salt and pepper. Allow them to sit for a couple of minutes and then toss with 1/4 cup vinaigrette. Set aside.
4. Fill a medium sized sauce pan with water and bring to a rolling boil. Using tongs, gently lower the eggs into the boiling water. This will lower the temperature of the water slightly; wait for the water to come back to a rolling boil and then turn the temperature of the burner down to low. Cook eggs at a very gentle simmer for 11 minutes. Fill a bowl with cold water; using tongs, remove the eggs from the boiling water into the cold water. Let cool, then peel, and slice in half lengthwise.
5. Put the tomatoes and onions into a bowl and toss with about 3 tbsp of the vinaigrette, and 1 tsp each salt and pepper.
6. Arrange the lettuce on a large serving plate. Arrange all the vegetables – potatoes, tomatoes, red peppers, green beans – and eggs in piles around the edges of the plate.
7. Toss the chicken with about 2 tbsp of vinaigrette and arrange in the center of the plate.
8. Serve the Chicken Salad Niçoise with the remaining dressing and croutons.