Peel and chop the carrots and potatoes into 2 cm cubes, setting them aside for even cooking.
Heat the oil in a large heavy-bottomed pot over medium heat, listening for a gentle sizzle as you add the diced onion. Cook for about 5 minutes until it becomes translucent and fragrant, with a slight golden hue around the edges.
Add the minced garlic to the pot, stirring for about 30 seconds until it releases a fragrant aroma and slightly softens.
Sprinkle in the curry powder, stirring constantly for 30 seconds to toast the spices and unlock their vibrant aroma, making the kitchen smell warm and inviting.
Add the chopped carrots and potatoes to the pot, stirring well to coat them evenly with the fragrant spice mixture. Cook for 3-4 minutes until the vegetables start to soften and the spices cling to their surfaces.
Pour in the coconut milk and add a splash of water if needed to cover the vegetables. Bring the mixture to a gentle simmer, then reduce the heat to low, cover the pot, and let it cook for 20-25 minutes, stirring occasionally.
Check the vegetables for tenderness by piercing a piece with a forkāif it slides in easily, the curry is ready. If the sauce is too thin, simmer uncovered for another 5 minutes to thicken slightly.
Season with salt to taste and squeeze in fresh lemon juice for brightness, stirring well to combine all flavors.
If using greens, stir them in now and cook for 1-2 minutes until wilted and vibrant in color.
Remove from heat and let the curry rest for 5 minutes; this allows the flavors to meld and the sauce to thicken slightly.
Serve the warm, velvety curry in bowls, accompanied by rice or crusty bread, and enjoy the comforting aroma and tender vegetables with each bite.