Combine the water, rinds, and bay leaves in a large pot. Bring to a boil slowly, occasionally stirring, so the rinds don’t stick to the bottom of the pot. Once the water has come to a boil, lower the heat and simmer, uncovered, for 1 1/2 hours. Remember to continue stirring every so often. Line a mesh strainer with cheesecloth to collect any of the little cheese bits and bay leaves left in the broth and strain the broth into a clean container. Gather the cheesecloth together and discard. This makes it much easier to clean the strainer.
If you plan on using the broth right away, season it to taste with sea salt and black pepper, and let it simmer until your pasta is ready. If you plan to use the broth later, let it cool completely, cover it, and store it in the refrigerator for up to 1 week or freeze for up to 3 months.
While the finished broth is simmering, bring a large pot of water to a boil for the pasta. Season with sea salt and add the pasta. Cook until al dente. Strain the pasta and divide it evenly among 4-6 serving bowls. Ladle in the broth until you have the soupy consistency you desire. Top with grated Parmigiano Reggiano cheese and some freshly cracked black pepper and serve.