Heat the oil in a heavy large skillet over medium-low heat. Add the shallots, garlic, salt, and pepper, and saute until tender, about 1 minute. Add the peas and saute until heated through, about 5 minutes. Stir in the prosciutto and cook for 1 to 2 minutes.
Whisk lemon juice and Dijon mustard in a small bowl.
When ready to serve, top arugula with pea mixture and dressing. Toss to mix.