Spread your work surface with parmesan. Lower pastry into an undercrust of 0.25 inches (5 mm). Shape into a rectangle of 1.5 inches x 3 inches (4 cm x 6 cm). Lay over a baking sheet covered with parchment paper or a lightly oiled plate.
Bake puff pastry for 25 minutes. Set aside.
Peel and slice vegetables up to your taste. Cook vegetables with chicken broth until al dente, so about 15 minutes. Meanwhile, mix vegetables with vinaigrette. Reduce chicken broth of an half at medium heat. Add milk. Reduce for 3 minutes.
Over a parmesan feuilletine, set vegetables, another parmesan feuilletine and again vegetables. Pour vinaigrette all around. Garnish with fresh herbs up to taste.