Dice the potatoes and place in a large pot. Fill with cold water and season liberally with salt. Set over medium-high heat and bring to a boil. Cook until fork tender, about 15 to 20 minutes. Drain and transfer to a large bowl. Allow to cool slightly.
Mash with a potato masher until somewhat smooth. Stir in the mustard, chives, egg, 1 teaspoon salt, 1/2 teaspoon black pepper, granulated garlic, onion, and paprika and mix until smooth. Stir in the ham, cheese and peas. With damp hands, form the mixture into 12 even patties, about 1-inch thick. Place the flour on a shallow dish and set aside.
Set a large baking skillet over medium heat with about an inch of oil. Allow to get hot. Meanwhile, dust both sides of the potato cakes with the flour and place a few at a time into the hot oil. Cook until golden brown on both sides, about 2 minutes per side. Transfer to a plate lined with paper towels and continue frying the rest. Keep warm in a 250°F oven.
To make the pesto, place the arugula, pine nuts, garlic, parmesan, a large pinch of salt and pepper and lemon juice in a food processor. Pulse a few times until chopped through. While the machine is running, slowly drizzle in the olive oil until the pesto is smooth and creamy. Give it a taste and adjust seasoning accordingly, adding more salt or pepper as needed.
If making the salad, in a large bowl, toss together the arugula, olive oil, vinegar, a small pinch of salt and pepper, parmesan and pine nuts until evenly combined.
Serve the potato cakes warm with the salad on the side, a drizzle of the pesto on top and a lemon wedge on the side. Enjoy!