Pre-heat the oven to 400ºF.
In a small pot, melt the palm sugar with 2 tbsp water until smooth. Add the tamarind paste and the fish sauce and bring to a simmer for about 2-3 minutes, then remove from the heat. Transfer to a different container and cool to at least room temperature.
Examine the branzino and see if you need to remove any fins or bones. Use a sharp knife to carefully cut 3 shallow slits in the skin at an angle. Repeat on the other skin side. Rub the skin of the branzino with neutral oil, then place on a parchment paper lined sheet pan. Season the skin and the inside of the fish with a pinch of kosher salt.
Rub the inside flesh of the fish with about 1 tbsp of the sauce per side, then repeat on both sides of the skin. You should use around 4 tbsp total (2 inside, 2 on skin).
Spread the ginger pieces and the scallion pieces along the flesh, and top with about 4 slices of lime. Fold the other side of the branzino over the limes, ensuring everything stays (mostly) inside the fish.
Roast the stuffed branzino in the 400ºF oven for 10-15 minutes, or until the skin is slightly crisp, the flesh is white and opaque, and/or the internal temperature reaches 145ºF. You may optionally put it under the broiler for 1-2 minutes to get a crispier skin.
Transfer the whole branzino to a serving plate or platter, then garnish with chopped cilantro and chopped peanuts. Set the quartered lime pieces on the side to squeeze as desired.