To make the puree, using a slotted spoon, transfer the cubes to the work bowl of a food processor fitted with the metal blade or the jar of a blender. Add the garlic and process until a smooth puree. If the mixture is too thick, add some or all of the cooking liquid, if necessary. If too thin, transfer to a clean saucepan and cook over low heat to evaporate some of the moisture. Add thyme leaves and pulse to combine. Taste and adjust for seasoning with salt and pepper. If needed, re-warm the puree over medium-low heat. Serve immediately.