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Warmth the vegetable oil in a medium skillet. Add the garlic and cook dinner over low warmth unless golden, about 1 minute. Add the shallot, carrot, bell pepper and chile and cook dinner over reasonable warmth, stirring infrequently, unless the carrot is softened, about 7 minutes. Add the lime juice, vinegar, brown and granulated sugars and chili oil and lift to a boil. Elevate far from the warmth and let frigid a little bit. Switch the contents of the skillet to a blender and puree. Season with salt.
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In a little skillet, toast the sesame seeds over reasonably high warmth unless golden, about 40 seconds; let frigid. In a astronomical 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 lend a hand.
Notes
Any extra dressing might perhaps perhaps perhaps also moreover be old with diverse assertive greens like arugula, or it might perhaps perhaps really perhaps perhaps also moreover be old as a sauce for grilled rooster, little or stout-flavored fish.