Preheat the oven to 450 degrees F. Line a baking sheet with parchment paper.
In a bowl, combine the shallots, vinegar and 1/2 teaspoon salt, and let sit for 5 minutes.
Dice 2 of the peaches, leaving the skin on. Using a mortar and pestle, pound the diced peaches to a coarse puree. Transfer the peach puree to the shallot mixture, whisk in 3/4 cup olive oil and a pinch of salt and pepper. Taste for balance and seasoning. Place the slices of prosciutto on the prepared baking sheet.
Place another sheet of parchment paper over the prosciutto and another baking sheet on top of that. The second baking sheet will prevent the prosciutto from curling up in the oven. Cook in the oven for 10 to 12 minutes. Remove from the oven and cool completely. The prosciutto will crisp up while cooling.
Roughly chop the Marcona almonds and place in a bowl. Whisk in the remaining 1/4 cup olive oil. Add a pinch of salt and pepper.
Cut the remaining 3 peaches in half, remove the pits and cut them into 1/4-inch-thick slices. Arrange the sliced peaches and arugula on a plate. Tuck in some crispy prosciutto. Using a vegetable peeler, shave some goat cheese and tuck some cheese in and over the salad. Drizzle some of the peach vinaigrette over the salad.
Sprinkle the Marcona almonds over that and finish by drizzling some honey over the whole salad.