Especially since you consider cavadil plural, I'm pretty sure
you have an Italian/American pronounciation of cavatelli that's
fairly common in the East, at least. Cavatelli are small pasta
shells that look a little like hotdog buns.
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Cavatellinis a pasta made from flour, eggs, and ricotta and
gnocchi is made from potatoes
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Orzo is a type of pasta that resembles rice.
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There are a huge number (over 400) of pasta types including
whole wheat, flour, sheets, strips, Fresca, and spinach. Other
pasta types are cavatelli, capunti, and corzetti with a complete
list found online at pasta sites like Garrubbo.