Wipe out pan and set over medium heat. Melt the remaining butter and add the paprika, thyme, shallots, and bay leaf; cook, stirring often, until shallots are soft, about 5 minutes. Add flour and cayenne and stir until mixture thickens, 1 minute. Whisk in milk and cook, continuing to whisk often, until sauce has thickened and coats the back of a spoon, about 10 minutes. Discard thyme and bay leaf and remove pan from heat.