
Step 1
Preheat oven to 400°. Heat oil in a large deep skillet over medium-high. Cook carrots, turning once, until golden brown in spots but still very firm and crunchy, about 6 minutes. Using a slotted spoon, transfer carrots to a plate. Reserve pan with oil.
Step 2
Mash lemongrass, garlic, chile, and ginger to a coarse paste with a mortar and pestle. (Alternatively, you can chop very finely with a chef’s knife.)
Step 3
Set reserved skillet over medium heat; add paste. Cook, stirring often, until paste starts to soften and is golden, about 3 minutes. Pour in coconut milk and fish sauce (if using). Season with salt; bring to a simmer. Remove from heat, add carrots, and bake in oven until carrots are tender and sauce is thickened, 25–30 minutes.
Step 4
Meanwhile, toast coconut flakes in a dry small skillet over medium heat, shaking pan occasionally, until golden, about 3 minutes. Transfer to a small bowl; wipe out skillet.
Step 5
Toast coriander seeds in same skillet over medium heat, shaking pan often, until slightly darkened and fragrant, about 2 minutes. Transfer to mortar and pestle and let cool, then coarsely grind (or lightly with flat side of chef’s knife). Add coriander and sesame seeds to coconut flakes; season lightly with salt. Crush coconut flakes with your hands until almost uniform in size with seeds.
Step 6
Transfer carrots to a platter and top with mint and some coconut dukkah. Reserve extra dukkah for another use.