How to Make It
Whisk together vinegar, lime juice, honey, and crushed red pepper in a bowl; set aside.
Toss together cabbage, sugar, and 1/4 teaspoon of the salt. Let stand 20 minutes at room temperature.
Heat oil in a medium skillet over medium. Add carrots, and cook, stirring often, until just beginning to soften, 3 to 4 minutes. Toss with remaining 1/4 teaspoon salt; transfer to a plate.
Prepare noodles according to package directions.
Working with 1 at a time, soak rice paper sheets according to package directions, and place on a dry paper towel on a work surface. Create a 4-inch long overlapping pattern of beets, radishes, and avocado in a horizontal line in center of sheet; top with 1/4 cup cabbage mixture, 3 tablespoons carrots, and 1/4 cup noodles. Tuck in sides of rice sheet, and roll up burrito-style. Place on a plate lined with damp paper towels. Repeat with remaining ingredients. Serve with sauce.