Peel and finely chop the onion. Warm a pan for 1 min. Add 1 tbsp olive oil and the onion. Season with salt and pepper. Cover, keep the heat very low and gently sweat for 10 mins till softened but still white.
While the onion sweats, halve and deseed the peppers and chilli. Finely chop them both. Stir them into the onions. Put the lid back on and sweat for another 5 mins.
Add 1 tsp each of the coriander and cumin seeds. Cook and stir for 1 min, then tip in the tin of tomatoes. Fill the tin with hot water (roughly 400ml water) and add that. Cover. Bring to the boil. Turn the heat down and simmer the soup for 5 mins to bring the flavours together. The veg should all be very tender.
Ladle into a blender and blitz till smooth, or use a hand-held blender. Zest and juice the lime. Swirl in the lime juice. Taste and add more salt and pepper if you think it needs it. Ladle into bowls and top with lime zest to serve.