Add both potatoes to a medium saucepan, cover with cold water and season well with salt. Bring to a boil over medium-high heat. Reduce the heat to medium and simmer until fork-tender, about 10 minutes. Drain well.
Meanwhile, heat the butter in a small skillet over medium heat until the bits at the bottom of the skillet are deep brown, about 7 minutes. Remove from the heat.
Transfer the potatoes to a ricer in batches and rice into a medium bowl. Add the butter, cream, vanilla seeds, lemon zest and 3/4 teaspoon salt and mix well with a rubber spatula to combine.
Heat the oil in a small pan over medium heat until hot. Add the prosciutto and cook, stirring often with a slotted spoon, until crispy and golden brown, about 3 minutes. Remove to a paper towel-lined plate to drain.
Transfer the mashed potatoes to a serving bowl and sprinkle with the crispy prosciutto before serving.