To make the marinade: In a medium bowl, whisk together the fish sauce, rice vinegar, sugar, and vegetable oil. Remove ¼ cup of this mixture and set aside. Add the red curry paste and continue to whisk until smooth.

In a large, resealable plastic bag, combine the marinade and steak and seal the bag, pressing out the excess air. Marinate in the refrigerator, turning once or twice, for at least 4 hours or overnight.

When you are ready to make the rolls, in a large bowl soak the rice-stick vermicelli in hot water to cover until softened and pliable, about 15 minutes.

Prepare a grill or preheat the broiler.

Discard the marinade and grill the steak on an oiled rack set 5 to 6 inches over glowing coals, about 5 minutes on each side for medium-rare. (Alternatively, broil the steak on the rack of a broiler pan about 3 inches from the heat for about the same amount of time.) Transfer to a cutting board and let rest for 10 minutes.

Drain the noodles in a colander, then rinse under cold running water and drain well again. Place the noodles in a medium bowl, add the ¼ cup reserved marinade, and toss to coat.

Thinly slice the steak on the diagonal.

Put a double thickness of paper towel on a work surface, and fill a shallow baking pan with warm water. Check the rice-paper rounds and use only those that have no holes. Soak 1 round in warm water until pliable, 30 seconds to 1 minute. Carefully transfer to the paper towels.

Arrange 3 cilantro leaves and 3 mint leaves across the bottom third (the part nearest you) of the soaked rice paper. Top with 1 slice of steak. Spread ¼ cup noodles on top of the steak and arrange 8 cucumber matchsticks and 6 green onion strips on top of the noodles. Fold the bottom of the rice paper over the filling and begin rolling it up tightly, stopping at the halfway point. Arrange 3 more mint leaves and 3 more cilantro leaves along the crease, then fold in the ends and continue rolling. Transfer the summer roll, seam side down, to a plate and cover with dampened paper towels. Make 9 more rolls in the same manner and serve, whole or halved diagonally, with the dipping sauce.