Preheat oven 400 degrees F.
Preheat a grill pan or outdoor grill on high. With a sharp knife, cut the thawed but chilled puff pastry sheet in to 4 squares and arrange on a cookie sheet and sprinkle with a little salt and pepper.
Cook the puff pastry according to package directions, or until golden brown all over, about 12 to 15 minutes.
While the puff pastry is cooking, season the skirt steak with extra-virgin olive oil, garlic, rosemary, salt and pepper. Grill meat 3 to 4 minutes on each side. Remove meat and let it rest 5 minutes to allow juices to redistribute.
While the steak is cooking, trim the woody ends off a small bunch of asparagus. Drizzle with extra-virgin olive oil and season with salt and pepper. As soon as the steak is off the grill and resting, add the asparagus to the grill.
Grill the spears turning frequently until the asparagus is tender, about 4 to 5 minutes. Remove the asparagus from the grill and cut into large 2-inch pieces.
In a bowl, toss together the grilled chopped asparagus, crumbled blue cheese, and chopped arugula. Season the mixture with balsamic vinegar, salt and pepper.
Slice the rested steak thinly across the grain. Top each golden brown puff pastry square with some steak slices. Top the steak with the asparagus salad and serve.