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.
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.
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.