Whisk all dressing ingredients together. Taste and adjust until sharp, sweet, and bold.
Soak sliced red onion in cold water for 5 minutes. Drain and pat dry.
Dice the mango and slice the cucumber on the diagonal into thin pieces.
Add mango, cucumber, red onion, and chili to a large bowl.
Pour dressing over the salad and toss gently to coat without mashing the mango.
Add mint and cilantro. Toss once more very gently.
Taste and adjust seasoning with salt and extra lime juice.
Serve immediately on a wide platter topped with sesame seeds and crushed nuts.