Heat the oil in a large heavy-bottomed pot over medium heat until shimmering and fragrant.
Add the finely chopped onion and cook, stirring often, until it turns golden and translucent, about 3-4 minutes.
Stir in the minced garlic and toast for 30 seconds until fragrant, being careful not to burn it.
Add the cumin, turmeric, and coriander, stirring constantly for about 30 seconds to toast the spices and release their aroma.
Pour in the diced carrots and potatoes, stirring well to coat them with the fragrant spice mixture.
Cook the vegetables for 5-7 minutes, stirring occasionally, until they start softening and develop a little color.
Pour in the coconut milk and vegetable broth, stirring to combine and scrape up any browned bits from the bottom of the pot.
Bring the mixture to a gentle simmer, then cover and reduce the heat to low. Cook for 20-25 minutes, until the carrots and potatoes are tender but not falling apart.
Uncover and simmer for an additional 5 minutes to thicken the sauce slightly, stirring occasionally.
Taste and season with salt and pepper, then squeeze in a little lemon juice for brightness, if desired.
Remove from heat and garnish with chopped cilantro. Serve hot with rice or naan, enjoying the comforting aroma and vibrant flavors.