1. Heat peanut oil in large nonstick skillet over medium-high heat. Ad carrot and peppers and stir-fry 2 minutes. Add ginger and garlic and stir-fry 2 more minutes. Add zucchini and squash and cook 3 additional minutes, making sure vegetables remain crisp.
2. Partly fill glass pie plate with hot water. One at a time, dip rice paper sheets in water until softened, about 10 seconds. Blot dry. Lay softened sheet on clean surface. Place a few cilantro leaves in center of each rice paper. Top with evenly divided vegetables; drizzle with Thai dressing.
3. Fold ends of rice paper over filling, then roll up tightly into neat cylinder. Set seam side down on large platter and cover with damp paper towel to keep moist.