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grows out of · the meal fulfilled
The Last Supper is a Passover meal. Jesus takes the bread and cup of a rescue from Egypt and gives them a new referent — his own body and blood — so the annual remembrance of one deliverance becomes the sign of a greater one.
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grows out of · the same words
Moses says 'the blood of the covenant' as he throws blood over the people at Sinai. Jesus lifts the cup and uses the identical phrase, adding one word: new.
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grows out of · the new covenant
Jesus does not invent the phrase. 'This cup is the new covenant in my blood' announces that Jeremiah's promise is now being enacted.