Heat the peanut oil in a small saucepan over medium-high heat until a deep-fry thermometer registers 350 degrees F. Add the sliced shallot and cook, stirring often, until golden brown, about 3 minutes. Remove with a slotted spoon and drain on paper towels; season with salt.
Whisk 2 tablespoons of the frying oil, the chopped shallot, lime juice, fish sauce, soy sauce, garlic, ginger and jalapeno in a large bowl. Add the watermelon and toss to combine. Let sit 10 minutes.
Add the cilantro, basil, mint and 2 tablespoons peanuts to the salad and season with salt; toss to combine. Top with the remaining 1 tablespoon peanuts and the fried shallot.