In a skillet over medium heat, warm 1 tablespoon of olive oil and 2 tablespoons of unsalted butter until melted and bubbling. Add finely chopped shallots and minced garlic, and sauté for about 3-4 minutes until they become soft and translucent.

Increase the heat to medium-high and add the well-trimmed chicken livers along with fresh thyme. Sear for about 5-7 minutes until browned on the outside but slightly pink in the center.

Pour in ¼ cup of brandy or cognac, scraping the bottom of the pan to release flavorful bits. Allow to cook down for about 2-3 minutes until most alcohol has evaporated.

Transfer the liver mixture to a food processor and add ½ cup of heavy cream and remaining ½ cup of unsalted butter. Pulse until smooth and creamy, about 1-2 minutes.

Strain the blended pâté through a fine sieve or mesh to remove bits. Transfer into a dish, smoothing the surface.

If desired, melt some clarified butter and pour a thin layer over the top of the pâté. Cover with plastic wrap and refrigerate for at least 4 hours, preferably overnight.