In a large pot, brown the chicken pieces in oil. Remove and set aside.
In the same fat, sauté the onion and garlic, then add the carrot, squash, and tomato, and cook for 5 minutes.
Return the chicken to the pot. Add water/broth, salt, pepper, and bay leaf. Bring to a boil and simmer covered for 30-40 minutes until the chicken is tender.
Remove the chicken, debone it, and shred the meat. Strain the soup (if you want a clearer broth) or leave the vegetables in (the traditional way).
In a bowl, mix the cornmeal, grated cheese, butter, a pinch of salt, and oregano.
Gradually add the hot chicken broth (from Step 1) until a firm yet workable dough is formed. Do not knead the dough; just combine it so it retains a grainy texture.
Shape the dough into small balls (about 1-1.5 cm in diameter). For an extra cheesy core, you can place a tiny piece of cheese in the center of each ball.
Bring the broth back to a boil (if strained, add the shredded chicken and vegetables back in).
Carefully drop the borí dumplings into the boiling broth. Cook them for 10-15 minutes. They are done when they float to the surface and the broth thickens slightly.
Taste and adjust seasoning if necessary.
Serve Vori Vori hot, sprinkled with fresh parsley or green onion.