Press Saute on the Instant Pot and let it heat for a minute. Add the ground beef and break it apart with a wooden spoon. Cook until it is browned all the way through with no pink remaining, about 5 to 6 minutes. If there is a lot of excess fat in the pot, tilt it slightly and spoon off most of it, leaving just a thin layer.

Add the diced onion, celery, and carrots to the pot. Stir them into the beef and cook for 3 to 4 minutes until the onion begins to soften. Add the garlic and stir for 30 seconds. Press Cancel.

Add the diced tomatoes with their juice, drained cannellini beans, beef broth, water, Italian seasoning, salt, pepper, red pepper flakes if using, and the Parmesan rind if you have one. Stir everything together and make sure nothing is stuck to the bottom of the pot. Secure the lid with the vent set to Sealing and pressure cook on High for 8 minutes.

When the cook time finishes, do a quick release by carefully turning the vent to Venting. Once the pressure pin drops, open the lid. Remove and discard the Parmesan rind. The soup will look a bit brothy at this stage, which is exactly what you want before adding the pasta.

Press Saute. Stir in the dry ditalini pasta. Cook uncovered, stirring every couple of minutes to keep the pasta from sticking to the bottom, for 7 to 8 minutes until the pasta is tender and the soup has thickened to a hearty, stew-like consistency. It should coat a spoon and not look watery.

Press Cancel. Taste the soup and adjust salt and pepper as needed. If it is thicker than you like, stir in a splash of broth. Ladle into deep bowls, scatter fresh parsley over the top, and finish with a generous pinch of grated Parmesan.