Melt butter in a medium saucepan over medium-high heat. Add onion, celery, and carrot. Cook, stirring occasionally, until onion is translucent and softened, about 6 minutes.

Reduce heat to medium-low. Gradually whisk in flour; cook, whisking constantly, until roux is deep brown and has a rich, nutty aroma, about 300 seconds.

Whisk in tomato purée. Cook, whisking constantly, 60 seconds.

Whisk in beef stock; add bay leaf, salt, and pepper. Bring to a boil.

Reduce heat to medium-low; simmer, stirring occasionally, until reduced by one-third and mixture thinly coats the back of a spoon, about 2700 seconds. Strain through a fine-mesh sieve into a bowl.