• Set the rice noodles in a large heatproof bowl.

In a medium sauce pot, bring 1½ quarts water to a boil. Pour the boiling water over the rice noodles and let soak until just tender, 6 to 7 minutes. Drain the noodles and rinse them under cold water; return them to the bowl and toss with 1 to 2 teaspoons oil to prevent sticking. Do not clean the pot.
While the water heats and the noodles soak, prepare the limes and chicken.

• Juice 1 lime.
• Cut the remaining lime into wedges for garnish.

In the same pot used for the noodles, combine the coconut milk, lime juice, and 1 cup water; season with salt and sugar, if using, and bring to a boil. Carefully lower the chicken into the boiling liquid and cook until opaque and cooked through, 3 to 5 minutes. Using a slotted spoon or tongs, transfer to a plate to cool, then using a fork, shred the chicken.
While the chicken cooks and cools, prepare the ginger dressing and remaining salad ingredients.

• Grate or peel and finely chop enough ginger to measure 1 teaspoon.

In a small bowl, stir together the dressing base, ginger, and as much sambal oelek as you like. Season to taste with salt.

• Trim the root end from each romaine heart.
• Coarsely tear the romaine leaves.
• Trim off the top and bottom of each mango; cut away the peel, then cut the flesh into two halves away from the pit. Cut each half in half lengthwise, then thinly slice crosswise.
• Coarsely chop the cashews.
• Cut the cherry tomatoes in half.
• Strip the basil leaves from the stems; coarsely tear the leaves.
• Coarsely chop the cilantro.

In a large bowl, combine the romaine, mangoes, cashews, tomatoes, basil, cilantro, and chicken. Add half the ginger dressing and 2 to 3 teaspoons oil and toss to coat. Season to taste with salt and more dressing, if needed.

For any paleo diners, transfer their portion of the chicken salad to individual bowls. Add the rice noodles to the remaining chicken salad, toss to combine, and transfer to individual bowls. Serve the lime wedges and the remaining dressing on the side.