In a large skillet, melt the butter over medium heat.
Add the chopped onion, minced garlic, and diced carrots.
Cook and stir for about 7 minutes until tender.
Transfer the mixture to a medium bowl and let cool for 15 minutes.
Meanwhile, cut the round steak into 4 equal portions.
Trim excess fat and place each piece between sheets of wax paper.
Pound until ¼-inch thick.
Divide the onion mixture evenly among the beef pieces.
Roll up each steak tightly, enclosing the filling, and secure with toothpicks.
On a plate, combine the flour, salt, and pepper.
Dredge the beef rolls in the flour mixture.
Heat the vegetable oil in the same skillet.
Brown the beef rolls on all sides.
Place the browned beef rolls in a 4-quart slow cooker.
Deglaze the skillet by adding the beef stock, tomato sauce, mustard, and Worcestershire sauce.
Bring to a simmer, stirring well.
Pour the sauce over the beef rolls in the slow cooker.
Cover and cook on low for 7–8 hours, until the beef is tender.
Notes / Tips / Wine Advice:
Serving Tip:Serve the rouladen with its rich sauce, accompanied by mashed potatoes or buttered spaetzle for an authentic German meal.Wine Advice:A bold German Spätburgunder (Pinot Noir) or a dry Riesling pairs beautifully with this slow-cooked dish.