Combine the shallots, mustard, vinegars, olive oil, salt, and pepper in a jar and shake vigorously to emulsify. This can also be done in a blender.
Cook the bacon in a medium-sized skillet over low heat to slowly render out the fat. Turn the heat up to medium, and continue cooking until the bacon is caramelized and crisp. Remove from the heat and drain on paper towels for several minutes. Chop and set aside.
While the bacon is cooking, prepare the soft boiled eggs. Allow the eggs to chill in an ice water bath for several minutes before peeling to avoid wilting the greens. Peel and slice the eggs lengthwise right before plating.
Arrange the arugula, bacon, eggs, almonds and Parmigiano on two plates. Drizzle with shallot Dijon vinaigrette and serve.