I was thinking Arby's, but couldn't go there today, so I decided to try my hand at one of my favorites at home.
1 pound thinly sliced roast beef
1 box (32 oz) beef broth
4 tbsp honey bbq sauce
1/2 cup Velveeta cheese
4 onion rolls
Place broth and roast beef into a sauce pan. Heat until it comes to a boil; boil for about a minute. Remove from heat. Heat Velveeta in a microwave or small pan, until melted; about 1 minute in microwave at 30 second increments adding 15 seconds if needed. Place 1 tbsp bbq sauce on bottom half of each bun. Top with 1/4 of meat per bun. Top each with melted cheese. Place top of bun.
I'm not sure how to make a saucier sauce with the cheese. I'll have to figure out the cheese to water ratio for an actual sauce for this; the cheese became firm quickly. I thought it would be smoother because it's a processed cheese substance, but I guess that new cheese (aged less than 10 months) would melt just as well. Perhaps next time I'll go with cheese slices. The honey barbecue sauce is similar to the Arby's sauce I like. I found a package of onion rolls, one that wasn't too firm like I have found some onion rolls to be. I just wish I had some french fries to go with this. I looked for curly fries, but didn't find any in the price range I prefer to pay.
Flavor Rating: Good, not as great as Arby's, but close enough.
Ease of Preparation: Easy, it took a couple of steps, but turned out well in the end.