Mondare, lavare e tritare il prezzemolo, l’aglio, la cipolla, le carote e il sedano. Battere il lardo a coltello. Immergere i pezzi di coda in abbondante acqua in ebollizione e quando l’acqua riprenderà bollore, togliere la carne. In una padella antiaderente riunire il lardo e il trito di verdure e lasciare soffriggere per qualche istante. In un tegame sufficientemente capiente aggiungere un filo di olio extravergine di oliva, portare a temperatura, unire la coda, insaporire con sale e pepe e rosolare fino a doratura. Sfumare la carne con il vino bianco, lasciare evaporare, abbassare la fiamma, aggiungere la polpa di pomodoro e qualche mestolo di brodo di verdure. Chiudere con il coperchio e cuocere a fuoco molto dolce (o infornare a 130°C) per circa 4 ore, aggiungendo altro brodo durante la cottura. A fine cottura separare la coda dal fondo, lasciarla intiepidire, spolparla con le dite e sfilacciarla, quindi riunirla alla salsa.
Cuocere i rigatoni molto al dente, unirli al condimento, mantecare con una generosa spolverata di formaggio Pecorino grattugiato, un po' di acqua di cottura della pasta e una macinata di pepe nero.
Impiattare e finire con un'ultima spolverata di Pecorino.
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