Cover eggs with cold water, bring to a boil, simmer 8–9 minutes, shock in ice water, then peel. Score the eggs lightly or cut them in half lengthwise.
Heat oil in a wide pan. Add mustard seeds; when they pop, add cumin seeds and curry leaves. Toss in green chilies. Your kitchen will smell like a vacation.
Add onions with a pinch of salt. Cook until translucent-golden. Stir in ginger-garlic paste; sauté till the raw smell disappears—about 60–90 seconds.
Add turmeric, chili powder, coriander powder, and fennel/pepper if using. Splash in a tablespoon of water so the spices don't burn. Cook till glossy and fragrant.
Stir in chopped tomato and cook till it breaks down and the oil glistens at the edges. Add a pinch of sugar if the tomato tastes sharp.
Pour in coconut milk and 1/3 cup water. Simmer gently—don't boil furiously or it can split. Season with salt.
Slide in the eggs. Spoon sauce over them. Simmer to let flavors mingle. Finish with garam masala, cilantro, and a squeeze of lime if you like.