Preheat the oven to 200 degrees . Place a rack on a baking sheet and transfer to the oven. In a large bowl, toss the sweet potatoes, ham, scallions, chopped parsley and flour; season with salt and pepper. In a separate bowl, beat the eggs with 1 teaspoon mustard. Stir the egg mixture into the sweet potato mixture.
In a large, heavy skillet, heat 2 tablespoons oil over medium-high heat. Working two at a time, add 1/3-cup mounds of sweet potato mixture, flattening into rounds. Lower the heat to medium and cook until golden, 3 minutes on each side; transfer to the baking sheet to keep warm. Add 2 tablespoons oil between batches.
In a bowl, whisk the remaining 2 tablespoons oil and remaining 2 teaspoons mustard. Add the parsley leaves, celery and celery leaves and toss to dress; season with salt and pepper. Serve topped with the warm fritters.