In a stockpot, melt the butter on medium heat. Add the onions, carrots, celery, and kosher salt. Reduce the heat to low and saute the vegetables for about 10 minutes, until soft and translucent. Sprinkle the vegetables with the flour and stir to combine, making sure the flour is well mixed into the butter. Cook, stirring constantly, for 1 minute.
Add white wine and cognac. Bring to a boil over medium-high heat, stirring constantly, for 1-2 minutes. Mixture will be thick. Add the stock, thyme, bay leaf, cayenne, and tomato paste. Bring to a boil, stirring vigorously to fully blend in the roux, and then reduce the heat to low and simmer for 20 minutes.
Strain the stock to remove all the solids and then return it to the pot. Add the milk and cream and bring the bisque back to a simmer. Remove the soup from the heat. Add in the chopped lobster meat and warm it through.
Serve the bisque topped with creme fraiche (if desired) and chives.