Cut top and bottom from the green papaya. Then, peel the green papaya with a vegetable peeler.
Once the dark skin has been removed, use the serrated peeler to create long strands of green papaya. Stop when you get to the seeds in the middle.
Repeat the process with the carrots. Place green papaya, carrots, and halved tomatoes into a large bowl or serving platter.
In a small bowl or Mason jar, combine fish sauce, lime juice, brown sugar, minced garlic, and crushed red pepper flakes. Whisk or shake dressing ingredients until combined.
Pour dressing over salad and toss to combine.
Top with chopped peanuts and fresh cilantro or parsley.