In a large pot, combine the water, lentils and bay leaf and bring to a boil. Reduce the heat to low and simmer for 20 minutes, or until the lentils are tender.
Drain, reserving 1 cup of the cooking liquid. Discard the bay leaf. Wipe out the pot with paper towels. Heat the oil in the pot and sautι the onions with the Aleppo pepper or pepper flakes over medium heat until soft, about 5 minutes. Add the lentils and saute  for 1 minute. Add the reserved cooking liquid, the stock and salt to taste, bring to a boil, reduce the heat to low and simmer for 10 minutes. Return the broth to boiling, add the pasta, increase the heat to medium and cook for 8 minutes, or until the pasta is al dente. Taste and adjust the seasonings, adding a few grindings of black pepper. Stir in the mint.
Ladle the soup into bowls, drizzle oil and a little vinegar over each serving and garnish with the mint leaves.