'priest choker' or 'priest strangler'[1]: 152 [2]) are an elongated form of cavatelli, or hand-rolled pasta typical of the Emilia-Romagna, Tuscany, Marche and Umbria regions of Italy as well as in the state of San Marino.
[1] Another explanation involves the azdora ('housewife' in the Romagna dialect), who "chokes" the dough strips to make the strozzapreti.
The azdora would express rage (perhaps triggered by the misery and difficulties of her life) and curse the local clergy, resulting in a pasta that could choke a priest.
[3] A third states that wives would customarily make the pasta for churchmen as partial payment for land rents (in Romagna, the Catholic Church had extensive land properties rented to farmers), and their husbands would be angered enough by the venal priests eating their wives' food to wish the priests would choke as they stuffed their mouths with it.
Another possible explanation is that following Sunday Mass, it was common for the priest to visit homes of the villagers and enjoy dinner with them.