In a deep fry pan or wok, heat the oil to 350 degrees F.
Deep fry the anchovies in two separate batches for 3 minutes, or until brown and crisp.
Remove the anchovies and place them on absorbent kitchen paper towels to drain the excess oil.
In a mixing bowl, combine the green mango, perilla leaves, mint leaves, Vietnamese mint, Asian basil leaves, chile, fried shallots, fried garlic, crisp anchovies, and 3 tablespoons of nuoc mam cham dipping fish sauce. Toss the mixture well, and transfer to a plate or shallow bowl and garnish with the crushed peanuts.
To make the dipping fish sauce: Combine the fish sauce, vinegar, sugar, and water in a saucepan and place on medium heat. Stir well and cook until just before boiling point is reached, then allow to cool. To serve, finely chop the garlic and chile and stir through with the lime juice.