Preheat your oven to 300°F. Line a large rimmed baking sheet with unbleached parchment paper.
Place the coconut chips on it in a single, even layer. Place the baking sheet in the oven and bake for 5 minutes.
Remove the baking sheet from the oven, stir the chips to redistribute them on the baking sheet, and return them to the oven for another 5 minutes or until they’re very lightly golden brown on the edges.
Transfer the chips to a wide, relatively flat bowl, add the bread crumbs, toss to combine and set the bowl aside to cool.
Make the shrimp.
Break the egg into a medium-size bowl.
Whisking constantly, pour the olive oil into the bowl. Continue to whisk until the mixture begins to form an emulsion (it will become creamy).
Add the gum free flour and whisk until a very thick paste forms.
Add 2 tablespoons of milk and whisk, adding up to one more tablespoon of milk to thin the mixture until it’s thickly pourable.
Add the salt and pepper, and whisk to combine.
Add the raw shrimp to the bowl, and mix gently to coat them in the batter.
Allow the shrimp to sit in the batter while you prepare the oil.
Place about 1/4-inch of frying oil in a heavy-bottom skillet and heat until rippling over medium heat.
Place the bread crumb and coconut mixture next to the stove, and a large plate, platter, or tray lined with paper towels next to that.
Remove the shrimp pieces one at a time from the batter and press each side into the bread crumb mixture firmly enough for them to stick.
Lower the heat to medium-low and place the prepared shrimp in the hot oil, one at a time without overlapping them in the skillet.
Allow the shrimp to fry for about 3 minutes or until golden brown on the underside.
Using tongs, carefully flip each shrimp and allow them to cook on the other side until golden brown underneath and cooked all the way (about another 2 minutes).
Remove the shrimp, place on the paper towel-lined plate or tray to drain, and repeat with the remaining shrimp.
Make the dipping sauce.
In a small bowl, combine all three ingredients and whisk them together until smooth.