Place oven rack in lower third of oven and preheat oven to 300 degrees.
In a nonstick pan, cook prosciutto in a drizzle of olive oil over medium heat until crispy. Let drain on a paper towel-lined plate and crumble when cool.
Line a quarter-size sheet pan with parchment paper. (See Notes if using a half sheet pan.) Add half the chips, layer with half the shredded cheddar, half of the brie, and half of the Parmigiano Reggiano. Drizzle generously with hot honey sauce. Sprinkle half of the crispy prosciutto over cheese and hot honey sauce. Top with remaining chips, shredded cheddar, brie, Parmigiano Reggiano, and crispy prosciutto. Drizzle second layer generously with hot honey sauce.
Heat nachos on lower rack for 10-15 minutes. Until cheddar cheese is melted and brie has started to melt. Remove from oven and add diced salami, fresh chives, and fresh arugula. Dollop with spoonfuls of fig jam.
Notes
If using a larger half sheet pan, skip the layering and just serve nachos in a single layer.