Whisk the coconut milk, fish sauce, lime zest, lime juice, sugar, curry paste, and pepper flakes in a medium bowl until the curry paste is fully dissolved and the sauce is smooth.

In a separate small bowl, stir together a teaspoon of the oil with the garlic and ginger to form a rough paste.

Heat the remaining two tablespoons of oil in a 12-inch nonstick skillet over high heat until the oil is shimmering but not smoking. Add the cauliflower, water, and salt, then cover and cook until the florets are just tender and look slightly translucent, about 5 minutes.

Remove the lid and continue to cook, stirring occasionally, until the liquid has evaporated and the cauliflower is tender and well-browned, about 8 to 10 minutes.

Clear a space in the center of the skillet, add the garlic-ginger mixture, and mash it into the pan with a spatula for 30 seconds until fragrant.

Stir the garlic mixture into the cauliflower and reduce the heat to medium-high. Give the coconut milk mixture a quick whisk to recombine, then pour it into the skillet and simmer until the sauce has thickened slightly and coats the florets, about 4 minutes.

Remove the pan from the heat and stir in the basil. Serve hot.