Toss cabbage and carrot with 1 teaspoon salt in a colander or large mesh strainer set over a medium bowl. Let stand until cabbage wilts, 1 to 4 hours. Rinse cabbage under cold running water (or in large bowl of ice water if serving slaw immediately). Press, but do not squeeze, to drain; pat dry with paper towels. (Cabbage can be stored in a resealable plastic bag and refrigerated overnight.)
In the bowl of a food processor, puree peanut butter, oil, vinegar, soy sauce, honey, garlic, ginger, and jalapeno until a smooth paste is formed. Toss cabbage, carrot, radishes, scallions, and dressing together in a medium bowl. Season to taste with salt. Cover, and refrigerate until ready to serve.