How to Make It
Heat the vegetable oil in a medium skillet. Add the garlic and cook over low heat until golden, about 1 minute. Add the shallot, carrot, bell pepper and chile and cook over moderate heat, stirring occasionally, until the carrot is softened, about 7 minutes. Add the lime juice, vinegar, brown and granulated sugars and chili oil and bring to a boil. Remove from the heat and let cool slightly. Transfer the contents of the skillet to a blender and puree. Season with salt.
In a small skillet, toast the sesame seeds over moderately high heat until golden, about 40 seconds; let cool. In a large bowl, toss the frisée with the papayas, water chestnuts, cashews and ginger. Add about 1/3 cup of the dressing and toss to coat. Mound the salad on plates, sprinkle with the toasted sesame seeds and serve.
Any extra dressing can be used with other assertive greens like arugula, or it can be used as a sauce for grilled chicken, shrimp or full-flavored fish.