In a saucepan, melt butter. Add milk and sugar. Stir and simmer on low heat until bubbles appear on the perimeter.
Add semolina and cook, stirring constantly, until thickened, about 3 minutes.
Add vanilla and stir to combine.
Place in a casserole dish or in individual ramekins. Chill for at least 30 minutes.
Serve, garnished with the walnuts.
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