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1
Melt the lard in a wide, heavy pot over a medium flame. Add the onion, celery and carrot. Cook, stirring, until the vegetables have softened and the lard has turned translucent around them — the fat should smell of sweet pork, not browning.
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2
Add the potatoes in their rough, irregular pieces and stir to coat in the lard base. Drop the Parmigiano rind into the pot. Pour in 1.2 litres of water and bring to a steady simmer. Cook uncovered until the potatoes are 80% done — a skewer meets resistance at the centre but the outer flesh gives. Some pieces will already be beginning to break apart into the liquid, which will have turned slightly opaque from released starch.
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3
Add the pasta directly into the potato broth. This is where the dish lives or dies: the pasta must finish in the starchy potato liquid, absorbing it and surrendering its own starch in return — the two starches together create the characteristic dense, porridge-like consistency that defines azzeccata. Stir frequently to prevent the pasta from clumping on the base. If the pot tightens too fast, add reserved hot pasta water, never plain cold water. The dish is ready when the pasta is fully cooked and a spoon drawn through the pot leaves a brief furrow before the mass closes back in.
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4
Remove the pot from the heat entirely. Discard the Parmigiano rind. Scatter the cubed provola affumicata over the surface and fold through once or twice — the residual heat will melt the cheese into golden threads without seizing. Cover the pot and rest for 3 minutes. The cheese should be visibly threaded through the mass, not pooled or rubbery.
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5
Serve directly from the pot into warmed bowls. The portion should mound slightly when spooned — if it spreads flat and liquid, the dish has been finished too wet.