Heat the vegetable oil in a large skillet over medium-high heat.
Add the beef cubes in batches and brown them on all sides, about 3-4 minutes per batch. Transfer browned beef to the slow cooker.
In the same skillet, add the sliced onions and cook over medium heat until caramelized and golden, about 15 minutes, stirring occasionally.
Add the minced garlic and cook for 1 minute more until fragrant.
Sprinkle the flour over the onions and garlic, stirring constantly for 2 minutes to cook the flour.
Stir in the brown sugar and tomato paste until well combined.
Slowly pour in the Belgian-style dark beer, scraping up any browned bits from the skillet bottom.
Add the beef broth, red wine vinegar, dried thyme, bay leaves, salt, and black pepper. Stir to combine and bring to a simmer.
Transfer the mixture to the slow cooker over the browned beef.
Place the slices of white bread on top of the stew in the slow cooker.
Cover and cook on low for 8 hours, until the beef is very tender.
In a small saucepan, melt the butter over low heat. Remove the bread slices from the slow cooker and spread each slice with Dijon mustard, then dip them briefly in the melted butter.
Remove the bay leaves from the stew and discard them.
Stir the mustard-coated bread slices into the stew to thicken and enrich the sauce. Let sit for 5 minutes to absorb.
Serve the stew hot, garnished with chopped fresh parsley.