In a medium saucepan, combine the chicken livers, onion, garlic, bay leaf, thyme, and 1/2 tsp 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 and set aside for 5 minutes.
Transfer the liver mixture to a food processor, discard the bay leaf and cooking liquid. Process until coarsely pureed, then with the food processor running, add the butter, 2 tbsp 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.
Serve on good crackers or slices of bread.