In a medium saucepan, combine the chicken livers, onion, garlic, bay leaf, thyme, and 1/2 teaspoon of salt.
Add the water and bring to a simmer. Cover, reduce the heat to low, and cook, stirring occasionally, until the livers are barely pink inside, about 3 minutes. Remove from the heat handset aside for 5 minutes.
Transfer the livers, onion, and garlic to a food processor, discard the bay leaf and cooking liquid. Process until coarsely pureed then with the food processor on, add the butter, 2 tablespoons at a time until well combined.
Add the cognac (if using), season and process until completely smooth.
Transfer into ramekins, cover in cling film, pressing down so the plastic touches the pâté and refrigerate until firm.
