Heat a large skillet over medium heat and add the olive oil.
Add the chopped onion and garlic and sauté for 2–3 minutes, until softened.
Add the water and butter, allowing the butter to melt.
Add the chicken livers and cook for 4–5 minutes, turning occasionally, until lightly browned on the outside but still slightly pink inside.
Add the salt and thyme, cover, and cook for another 5–7 minutes, until just cooked through. Avoid overcooking.
Remove from heat and allow the mixture to cool completely.
Transfer to a blender or food processor and blend until smooth. Adjust seasoning if needed.
Spoon the pâté into a serving dish and smooth the surface.
Scatter the soaked cranberries or raisins over the top.
Pour over the melted butter to seal, then garnish with fresh thyme.
Refrigerate until set before serving.