Step 1 On a lightly floured board, roll the puff pastry out into a rectangle measuring about 8 by 16 inches; the dough will be just under one-fourth-inch thick.
Step 2 Using a 4-inch round pastry cutter, cut 8 rounds out of the dough (if you don't have a round cutter that size, use a bowl as a guide, or adjust the size of the vol-au-vents using what you have on hand). Using a 2 1/2-inch round pastry cutter, cut a circle out of the center of each of 4 rounds.
Step 3Assemble the vol-au-vents: Place the 4 whole rounds on a parchment-lined baking sheet, leaving an inch of space between each round. Lightly brush the rounds with the beaten egg, then place a ring of dough (one of the rounds with the circle removed from the center) directly on top of each whole round. Brush on top with the egg wash. Prick the center of the vol-au-vents with a fork to keep them from puffing too much. Place the baking sheet in the refrigerator to chill for about 20 minutes. Meanwhile, heat the oven to 425 degrees.
Step 4Bake the vol-au-vents until well puffed and golden-brown, 25 to 30 minutes. Remove from heat and set aside to cool. The vol-au-vents can be made up to 5 hours in advance.
Step 5In a medium saute pan, heat the canola oil over medium-high heat. Add the prosciutto and cook until crisp, stirring frequently. Remove from heat and drain the prosciutto on paper towels.
Step 6In a medium bowl, season the goat cheese with a pinch of salt and several grinds of black pepper. Stir in the chives, and adjust the seasoning and flavoring as desired.
Step 7In a medium bowl, whisk together the olive oil, vinegar and Dijon mustard. Whisk in the shallots and season to taste with one-fourth teaspoon salt and a few grinds of black pepper. Taste and adjust the dressing as desired. This makes a scant one-half cup vinaigrette, more than is needed for the rest of the recipe. The rest of the dressing will keep, covered and refrigerated, for up to 5 days.
Step 8Assemble the salads. In a large bowl, toss the shoots with a few tablespoons of the vinaigrette to lightly coat. Divide the goat cheese between the vol-au-vents, spreading the cheese over the base of each. Top the cheese with salad, and sprinkle over the crisp prosciutto crumbles. Serve immediately.