Thinly slice the cabbage in a food processor using the 4mm slicing disk (see the box at right) or by hand; you should have about 8 packed cups. In a colander, toss the cabbage with the shallot and 1 tablespoon kosher salt. Lay a plate that fits inside the colander on top of the cabbage and set a heavy can or jar on top of the plate. Drain the cabbage in the sink or over a bowl for 30 minutes.
If using a food processor, switch to the grating disk and grate the mango (see the bottom right photo in the box at right) or cut it into very thin (julienne) strips by hand; you should have 1-1/2 to 2 cups. Put the mango in a large bowl.
In a small bowl, mix the lime juice, oil, fish sauce, garlic, chile, and sugar.
Turn the cabbage out onto a clean dishtowel or some paper towels and pat it thoroughly dry. Toss the cabbage with the mango, herbs, and dressing. Season to taste with more kosher salt and lime juice if needed. Sprinkle with the peanuts and serve immediately.