Pat the beef cubes dry with paper towels and season thoroughly with salt and black pepper.

Toss the beef cubes with all-purpose flour until lightly coated, shaking off any excess.

Heat 2 tablespoons of butter in a heavy-bottomed Dutch oven over medium-high heat and brown the beef in batches until a dark crust forms; remove and set aside.

Add the remaining tablespoon of butter and the sliced onions to the pot, cooking on medium-low heat for 20 minutes until deeply caramelized.

Pour the Belgian ale into the pot to deglaze, scraping the fond from the bottom of the vessel.

Return the beef to the pot and add the beef stock, brown sugar, red wine vinegar, thyme, and bay leaves.

Spread the Dijon mustard onto the sourdough bread slices and place them mustard-side down on top of the liquid.

Cover with a tight-fitting lid and simmer on low heat for 2.5 to 3 hours, or until the beef fibers are tender.

Discard the bay leaves and thyme sprigs, then stir the disintegrated bread into the sauce to achieve the final thickened consistency before serving.