I tried something new, and it didn't come out perfectly because of my weak searing and dredging skills, but it is okay. Roasts were on sale. Don't stress about exact amounts. This will take refining.
Serves four people at about 650 calories and $2.00 each, but takes about 6 hours to make (you don't have to do anything for 5 of those hours).
1.7 lbs chuck roast - @ $2.39/lb = $4
1 cup all-purpose flour - @ $3/5lbs = ~$0.17
1/2 lb carrots - @ $1/lb = $0.50
3 stalks celery - @ $1.50/head = ~$0.50
6 red potatoes - @ $3/5lbs bag = ~$1.80
2 onions, regular - @ $1/lb = ~$0.50
1 tbsp garlic, minced - 1/42 of a jar @ $3/jar = $0.07
2 tbsp vegetable oil - @ $4/96tbsp bottle = $0.08
1 tsp oregano - @ $1/bottle = ~$0.05
2 tbsp red wine vinegar - @ $2/25tbsp bottle = $0.08
1/4 cup red wine - @ $15/5L box (Almadine Cabernet Sauvignon) = $0.19
splash of Worcestershire sauce - ?
2 paper towels - @ ~$1.00/roll = ~$0.03
Prep: Cut the beef into chunks 2-3" on each side. Take this opportunity to cut off the chunks of fat from the beef, and discard them. Slice up the carrots, celery, and onions. Dry the beef chunks on paper towels.
Cooking: Heat the oil in a skillet or pot. Brown the dried beef chunks for 3 minutes on each side (this may take 2-3 shifts as all the beef won't fit in the skillet at once). Dredge the beef in flour to coat, then return to the skillet for a couple more minutes to cook the flour on. Put the beef in your slow cooker or dutch oven. Put the sliced carrots, celery, onion, garlic, and oregano in the skillet. Stir fry the veggies together for a few minutes, then dump them on top of the beef. Mix your wine, vinegar, and Worcestershire sauce together in the skillet to deglaze it, then pour the liquid on top of the veggies. Add the potatoes, cover, and set to cook at low temperature for 5 hours, 325 F if using an oven.
Notes: I would absolutely use more wine. That was just all I had. Almadine boxed wine is surprisingly good for the price, and keeps well. Smaller potatoes will cook through and be soft, but larger potatoes will still be firm. I inadequately seared and dredged my beef, and some of the chunks were dried out after cooking. Water will cook out of the vegetables and meat. You may option to pour out all the liquids after cooking, and mix in a little flour or corn starch to form a gravy, but I do not have good instructions for that.
After some research, I believe that my trouble browning the beef was related to my use of a low quality non-stick skillet. I think this has caused several problems with my cooking over the years, and I am just now finding out about the benefits of aluminum-core stainless steel cookware and cast iron. Unfortunately, great cookware from All Clad or even Cuisinart is expensive beyond the theme of this blog. Perhaps the Salvation Army or similar facilities can provide low-cost decent-quality cookware. Lodge sells a very highly reviewed 12" cast iron skillet for $19, as well as other relatively inexpensive cast iron cookware, but these require careful use and maintenance. I will return to this topic in the future.