How to Make It
Preheat oven to 400°F. Cut the sweet potatoes lengthwise into 1/4-inch-thick slices, discarding the two side edges of the sweet potatoes that are rounded. Place slices on a baking sheet and bake until the outside is slightly dry but the center is tender and can easily be punctured with a fork, about 35 minutes. After baking, transfer sweet potato pieces to a cooling rack so they can cool without developing moisture on the surface.
While sweet potatoes are in the oven, whisk together lemon juice, 1/2 tablespoon of olive oil, mustard, and salt in a bowl. Set aside.
Add 1 tablespoon of olive oil to a nonstick skillet and heat over medium. Fry eggs 2 at a time until the white is cooked through and the yolk is still a little runny. Transfer to a paper-towel lined plate while you prepare the remaining eggs. Repeat frying process with remaining olive oil and eggs.
Place sweet potato pieces in a toaster to rewarm them. Toss the arugula in the lemon juice mixture. Top a toasted piece of sweet potato with some of the dressed arugula, a fried egg, and some freshly cracked black pepper and parmesan to garnish. Serve immediately.
Try to buy the most symmetrical and tubular sweet potatoes you can find for even slices.