Peel and chop the carrots and potatoes into roughly 1-inch cubes, ensuring they are uniform for even cooking.
Heat vegetable oil in a heavy-bottomed pot over medium heat until shimmering and fragrant, about 1 minute.
Add the finely chopped onion and cook, stirring occasionally, until golden and soft, about 5 minutes, releasing a sweet aroma.
Stir in the minced garlic and grated ginger, cooking until fragrant, about 30 seconds, making the kitchen smell warm and spicy.
Add the ground cumin, turmeric, and red chili flakes, toast briefly for about 30 seconds until spices release a smoky aroma.
Introduce the chopped carrots and potatoes into the pot, stirring well to coat them with the fragrant spices, and cook for 2-3 minutes until they start to look glossy.
Pour in the coconut milk and add a splash of water, stirring gently, then bring the mixture to a gentle simmer over medium-low heat.
Cover partially with a lid and let simmer for 20-25 minutes, stirring occasionally, until the vegetables are tender and the sauce has thickened slightly.
Taste the curry, then season with salt as needed and squeeze in fresh lemon juice to brighten the flavors.
Remove from heat and let the curry rest for 5 minutes to allow flavors to meld and thicken further.
Give the curry a gentle stir, then serve hot over rice or with crusty bread, garnished with herbs if desired.