Step 1In a small bowl, combine the vinegar, sugar and salt, and stir until the sugar and salt have dissolved. Add the carrots and let stand for at least 20 minutes before serving. This makes about one-half cup pickled carrots. If not using right away, cover and refrigerate for up to a week. Drain the carrots well before using.
Step 1In a small bowl, combine the fish sauce, sugar, vinegar or lemon juice, and one-half cup water, and stir until the sugar has dissolved. Add the garlic and chiles, and stir to combine. This makes about 1 1/2 cups flavored fish sauce, more than is needed for the remainder of the recipe. The sauce will keep, refrigerated, up to 1 week if made with vinegar or up to 2 days if made with lemon juice.
Step 1In a small saucepan, heat the oil over medium-high until it registers 275 degrees on a deep-fry thermometer. Add the shallots and cook, stirring, until light golden brown, about 8 minutes. Using a slotted spoon, transfer the shallots to a paper towel-lined plate to drain.
Step 2Increase the heat to high and place a fine-mesh sieve over a heat-proof bowl. When the oil registers 350 degrees, add the fried shallots and cook just until they are crispy and well-browned, 1 to 2 seconds, watching carefully so the shallots don't burn.
Step 3Immediately pour the oil and shallots through the sieve to stop the cooking, then transfer the shallots to a paper towel-lined plate to drain. This makes about 1 cup fried shallots. Reserve the oil for another use. The shallots will keep, stored in an airtight container, for 1 day, but they're best the day they are made.
Step 1In an 8-inch frying pan, heat the canola oil over high heat until it registers 350 degrees on a deep-frying thermometer. Carefully add the tofu slices and fry, turning once, until golden brown on both sides, 10 to 15 minutes. Using a slotted spoon, transfer the tofu to paper towels to drain. When cool, cut into strips one-fourth-inch wide.
Step 2In a large bowl, combine the papaya, rau ram, cucumber, celery, carrot and tofu strips. Pour the flavored fish sauce and shallot oil over the top and toss to coat evenly. Transfer to a serving platter and garnish with the peanuts and shallots. Serve immediately.