Heat a large cast iron skillet over medium high heat. Add bacon and cook until brown and crispy, about 6-8 minutes. Drain excess fat; transfer bacon to a paper towel-lined plate.
Place potatoes in a large saucepan and cover with cold salted water by 1 inch. Bring to a boil and simmer until just tender, about 7-10 minutes; drain well.
To assemble the salad, place arugula in a large bowl, top with bacon, potatoes, eggs, avocado and Parmesan. Pour the mustard vinaigrette on top of the salad and gently toss to combine.
For the Mustard Vinaigrette
In a medium bowl, whisk together olive oil, vinegar, mustard and shallot. Season with salt and pepper, to taste.