Dice the onion and chop the garlic. Cut the pork belly into slices.
In a heavy based pot, sautee the onions first in a little sunflower oil till they're translucent. Add the pork belly and garlic. Sautee till the pork is cooked on all sides.
Pour in the dashi stock just a little first to de-glaze the bits stuck at the bottom. Pour in the rest of the dashi stock and add carrots. Let it come to a boil and simmer for about 10 - 15 mins till the carrots are soft.
Add mirin and pepper. Add hard boiled quails' eggs just before dissolving miso.
Turn the heat off and dissolve miso into the soup. Sometimes certain miso can be quite salty in itself and you might not need soy sauce. I omitted mine. But always taste and check the seasoning.
I used a grainy type of miso here because it's all I have but the original recipe calls for white miso.
Serve hot in bowls scattered with some chopped scallions on top and shichimi pepper if you'd like.