Prepare Dipping Sauce and set aside.
Place a small nonstick skillet over high heat. Heat dry skillet until very hot. Sear tuna in skillet, 1 minute per side, or to desired doneness. Remove from skillet and slice into 8 log-shaped pieces. Set aside. In a medium bowl, soak rice sticks in hot tap water 10 to 15 minutes, until soft. Drain noodles thoroughly. Set aside.
Working one wrap at a time, briefly immerse rice paper in a shallow bowl of warm water, about 10 seconds (don’t leave paper in the water too long, or it will tear). Remove and place on clean kitchen towel. The paper will seem a bit stiff, but it will soften as you work with it. In the bottom third of each round, place 2 tablespoons grated carrots, then 3 or 4 scallion slivers, 4 or 5 cucumber strips, a slice of avocado, and a piece of seared tuna. Top with a generous sprinkling of mint and cilantro. Place a small mound of rice sticks on top. Fold in the left and right sides of the round. Begin rolling up from the bottom (roll tightly, but be careful not to tear the rice paper). Place each cigar-shaped roll on a platter. Cover with a damp kitchen towel until you are ready to serve.
The rolls are best served immediately, but they can be refrigerated, tightly covered, up to 2 hours before serving. To serve, cut each roll in half on the diagonal and serve with Dipping Sauce.
In a small bowl, combine sugar, chile, gingerroot, lime juice, and fish sauce. Mix well to combine flavors. Set aside.