Shallot oil and fried shallots:
1 cup vegetable oil
1 medium papaya
1 medium carrot
1/3 cup coarsely chopped fresh mint
1/3 cup coarsely chopped fresh cilantro
1/3 cup coarsely chopped fresh basil
3 teaspoons lime juice
2 teaspoons sugar
1 teaspoon fish sauce
2 teaspoons shallot oil
1 serrano chile, seeded and finely chopped
1 clove garlic, peeled and finely chopped
2 tablespoons finely chopped peanuts
Shallot oil: Peel shallots and slice them thinly. Put them on a baking sheet and place them in the sun to dry for two hours or put them in a 200°F oven for 15 minutes with the door slightly ajar (put a wooden spoon in the door to keep it partially open). Heat the oil in a small saucepan until warm (about 200°F). Add the dried shallots and cook them slowly, stirring gently from the edge of the pan into the center, until they turn a light golden color, about 5 minutes. Turn off the heat and remove shallots to a tray lined with paper towels. Cool the oil and store it, refrigerated, in an airtight container for up to one month.
Salad: With a vegetable peeler, shred the papaya and the carrot. Put them in a medium bowl with the herbs and toss gently with your hands.
Dressing: In a small bowl, whisk together the lime juice, sugar, fish sauce, shallot oil, chile and garlic.
Pour dressing over salad mixture and toss well. Divide among 4 salad plates and garnish with peanuts and fried shallots.