Preheat the oven to 425°F (220°C).
Scoop out the seeds and fiber from the cavity of the squash with a spoon, then cut into 1-inch wedges (no need to peel it, and watch the video for safe cutting techniques). Place the squash on a large plate.
1.5 lb Kabocha squash (about half a medium squash)
Prep the garlic:Cut the root end off the garlic and crush the cloves with the flat of your knife until the cloves are broken into big chunks. Remove the peel, and tear apart or chop any chunks that are too big. 5-6 garlic cloves
Make the glaze:In a small pot, add the oil and garlic and turn heat on to medium low. Once the garlic is bubbling, cook for about 2 minutes, stirring frequently, until they start to turn golden. Turn off the heat and remove from the oil. Be sure to remove ALL the little bits of garlic otherwise they will burn in the next step. 2 tablespoon vegetable oil
To the same pot, add palm sugar and cook until it melts, then turn off the heat. OR if you want a deeper caramel flavour, keep the sugar cooking a bit longer until the colour darkens slightly and then turn off the heat. (If you chose to further caramelize the sugar, then when you add the soy sauce it will splatter aggressively, and you may need to add a splash of water to thin out the glaze) 3 tablespoon palm sugar
Take the pot off the heat then add the soy sauce, (it will splatter vigorously), and once the splattering settles you can stir to mix. If it is thick, add about 1 tablespoon of water to thin out the glaze so it can be easily brushed onto the squash. Add the pepper, then throw the garlic chunks back in to coat in the glaze.
1 ½ tablespoon soy sauce, ¼ teaspoon ground black or white pepper
Brush this glaze over the squash on both sides, then place them on a parchment-lined baking sheet in one layer. Be careful to get as little glaze as possible on the baking sheet cuz it'll just burn in the oven.
Put the garlic chunks inside the curve of the squash pieces, shaking off excess glaze before placing them down—this will protect them from over-browning.
Roast for 10 mins, then take the squash out and brush with more glaze on both sides; then roast them for another 10-15 minutes or until fork-tender. If the garlic is starting to get too dark, you can take them out first. To check for doneness, pierce the thickest piece with a fork and it should go right through without resistance.
While the squash roasts, make the basil oil: Add the basil, a pinch of salt and oil into a mortar and pestle and grind to bruise and blend the basil with the oil. You can also just blend everything in a small food processor, but you may need to make a bit more basil oil than you need to make it blend effectively.
3 tablespoon neutral flavoured oil, A pinch of salt, ¼ cup finely julienned Thai or regular basil
AssemblePlace the squash on a serving platter in one layer and scatter the garlic pieces on top. Brush or drizzle the remaining glaze on the squash, then drizzle with basil oil. Serve warm or room temperature.