Add salted water to a medium pot and add the sunchokes. Bring to a boil over high heat. Reduce the heat to medium-low and simmer for 20-25 minutes. Remove from the heat and drain. Set aside until they are cool enough to handle.
In a small bowl, add the orange juice, Dijon mustard, and red wine vinegar, and whisk. Slowly add the olive oil, season with salt and pepper, and whisk to combine. Set aside.
Preheat the oven to 375°F. On a cutting board, and when cool enough to handle, smash the sunchokes with the palm of your hand.
Heat the olive oil in a large skillet over high heat. Add the sunchokes to the pan, season with salt and pepper, and cook, cutting them into large chunks with a wooden spoon, for 10 minutes. Remove from the heat. Transfer to a large baking sheet and sprinkle the prosciutto over the top. Place in the oven and cook for an additional 10 minutes. Remove from the heat.
Place the arugula in a large bowl. Add the sunchokes and prosciutto to the bowl. Toss with the vinaigrette until combined.
Transfer the salad to a large serving platter and serve immediately.