Meaning
To prepare a meal — especially a hearty, generous, or improvised one thrown together from whatever is on hand — and, as a noun, the dish itself. To 'cook up something' implies more warmth and effort than plain cooking, often a big pot to feed many people or a spread pulled together for company or a gathering. The particle 'up' lends a sense of abundance and completeness, and a good cook-up is an act of hospitality as much as of feeding.
Examples
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Mi a go cook up sinting nice fi di whole family tideh.
I'm going to cook something nice for the whole family today.
'a go' marks the near future; 'sinting' means 'something'.
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Mek wi cook up likkle rice an peas an chicken.
Let's cook up some rice and peas and chicken.
'mek wi' is the hortative 'let us'; 'likkle' means 'a little/some'.
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Dem cook up a big pot a food fi di nine night.
They cooked a big pot of food for the nine-night wake.
A 'nine night' is a traditional Jamaican funeral gathering held nine nights after a death.
Origin
From English 'cook' with the particle 'up' signalling completeness and abundance, a common Caribbean construction.
How it’s used
Everyday. Implies more effort and generosity than plain 'cook'; often used when feeding many people or making a spread.