Heat the oven to 300°F. Strip the kale leaves from the stems and tear each one into a few pieces. Toss with the olive oil and some salt, and spread them out on a large rimmed baking sheet so that they overlap as little as possible; use two baking sheets if you have them. Bake, tossing once or twice, until the kale is very crisp, 12 to 15 minutes. (If you’re using two baking sheets, swap them halfway through cooking so they have equal time on the upper and lower racks.) Set the kale aside. This step can be done up to a day ahead of time; just let the kale chips cool completely, then store in an airtight container until you’re ready to use them.
Lower the oven to 200°F. Put the squid in a bowl and add the buttermilk and 1/2 teaspoon of salt and stir to combine. The squid should be fully submerged. Set aside.
Put 2 inches of vegetable oil in a large, heavy-bottomed Dutch oven or skillet over medium-high heat. You’ll start frying at 375°F, so keep an eye on the temperature; I like to use a candy thermometer clipped to the side of the pot.
While the oil heats, line a rimmed baking sheet with paper towels and put the flour in a large, shallow bowl, or whatever you want to use for dredging. Transfer the Lemongrass-Fish-Sauce Caramel to a small saucepan and set it over low heat to warm up. Transfer half of the squid to the bowl of flour and toss to coat; some buttermilk will drip into the flour and form little clumps, which is exactly what you want. Press some of those clumps onto the squid; just make sure to separate any pieces that are stuck together, and shake off any excess flour (a mesh colander can be useful for this).
When the oil reaches 375°F, carefully add the dredged squid to the oil. Fry, gently stirring once or twice to make sure the pieces are separated and submerged, until golden and very crisp, 3 to 4 minutes. Transfer the squid to the paper-towel-lined baking sheet and put it in the oven to stay warm. Repeat the dredging and frying process with the second half of the squid.
When all the squid is fried, transfer it to a large mixing bowl of servings platter. Pour the Lemongrass-Fish-Sauce Caramel over the squid and toss to coat. Add the crunchy kale and basil leaves, and gently toss one more time. Serve immediately with lime wedges.