In a large bowl, combine the lime juice and the sliced shallot. Allow to sit and lightly pickle while you prepare the rest of the salad.
Using the flat side of a knife, mash the chilies, garlic, and salt to a fine paste (can use a mortar and pestle or spice grinder, if you have one). Mix the chili-garlic paste, the sugar (adjust based on how sweet your honeydew is), and the fish oil into the lime/shallot mixture. Stir to combine.
Add the honeydew and 4 tbsp each of the cilantro, mint, and peanuts to the bowl with the dressing. Toss to combine. Sprinkle with the remaining 1 tbsp of cilantro, mint, and peanuts right before serving.