Place the chicken wings, feet, and necks in a large pot. Cover with enough water to just cover the chicken. Place over low heat and allow to come to a simmer. This should take about 1 hour. Allow this to simmer for 4 hours. As it cooks, remove any scum that forms at the top, but avoid moving the chicken too much, and add additional water as it reduces during the cooking time.
After the 4 hours have passed, add the garlic, scallions, onion, and carrot to the pot. Allow to simmer for another 2 hours. Continue to remove any scum that rises and add additional water as it reduces.
After the cook time has passed, carefully remove all the solid items from the broth. Add the dashi to the chicken broth and stir together. Transfer to an airtight container and allow to cool completely.
Place in the refrigerator overnight to allow the fat to solidify on the surface. The next day, remove the fat and set aside for the chicken oil. The broth can be stored in the refrigerator for 1 week.