Put the potatoes in a medium pot and cover with water. Bring to a boil over high heat, then reduce and simmer for 25 minutes, or until fork tender. If the potatoes are really big it may take 35-45 minutes. When done, rinse potatoes under cold water to stop the cooking, and chop into bite size pieces. Set aside

While the potatoes are simmering, heat the broiler to high, and brush a rimmed baking sheet with olive oil.

Make the dressing in a small bowl by whisking together the vinegar, mustard, and ¼ teaspoon each of salt and pepper. Slowly pour in ¼ cup of the olive oil, whisking constantly, to emulsify. It will be nice and thick when done. Set aside.

Pour some breadcrumbs into a shallow bowl. Set aside. In a second shallow bowl, whisk together the egg and ¼ teaspoon each salt and pepper. Set aside. Slice the goat cheese into 1” thick rounds, and then flatten with the palm of your hand into ½” thick disks. Dip the cheese disks into the egg mixture, then into the breadcrumbs to lightly coat. Place the breaded cheese disks onto the oiled baking sheet and lightly brush the top of them with olive oil.

Place the cheese disks into the oven and broil until nice and crisp and golden brown, about 5 minutes.

Place the salad greens and chopped potatoes into a large bowl and add the dressing in increments, tossing to coat, until your desired flavor is reached. Serve and top with the cheese crisps.