In a medium bowl, combine fish sauce, lime juice, brown sugar, grated garlic, and Thai chilies. Whisk together until sugar dissolves.

Use a mandolin slicer to thinly slice the red onion and a 'Y'-peeler to julienne the carrot and green mangoes.

In a large mixing bowl, add the sliced red onion, julienned green mangoes, and shredded carrot. Toss gently.

Pour the dressing over the vegetable mixture and gently toss until all ingredients are coated.

Fold in the chopped cilantro, being careful to not bruising it.

Taste the salad and adjust the seasoning with more lime, fish sauce, or sugar as needed.

Serve the salad immediately to maintain its crunch and freshness.