In a large sauté pan or medium pot, melt the butter over medium-low heat. Add the onion, celery, and carrot. Season with kosher salt, cover, and cook gently for about 10 minutes, stirring occasionally, until the vegetables are very soft and fragrant.
Pour in the tomatoes with their juice and a pinch more salt. Stir to combine and bring to a boil. Reduce heat to low, add 1 cup of the chickpeas, and blend until smooth using an immersion blender. Taste and adjust seasoning—it should already taste great at this point.
Carefully return the sauce to a low boil (it may splatter). Stir in the remaining 2 cups chickpeas, chopped spinach, Parm rind, and dried ditalini. Reduce to a gentle simmer—aim for a slow bubble every 10 seconds or so.
Let it simmer for about
20 minutes, stirring occasionally, until the pasta is fully cooked and the sauce has thickened. The pasta will release starch as it cooks, so the sauce will naturally tighten up over time. Add a splash of water here and there as needed to keep the texture in that Goldilocks zone—not too thick, not too runny.
Remove from heat and let it sit a minute. Serve in bowls and top generously with grated Parmigiano Reggiano.