Melt butter in a medium saucepan over medium heat. Add shallot and cook for 3 minutes until softened.
Stir in flour and cook for 4 to 5 minutes, stirring constantly, until the roux turns light hazelnut brown without dark specks.
Whisk in the 3 cups warm stock a little at a time, scraping the bottom until smooth. Add thyme, salt, pepper and Worcestershire.
Simmer gently for 8 to 10 minutes, stirring often, until the gravy coats a spoon. Serve immediately or transfer to a shallow container and refrigerate within 2 hours for up to 2 days.
Reheat chilled gravy in a saucepan, whisking in the reserved stock a little at a time as needed, until it reaches a full simmer and 165°F. Serve hot.