Hello Brian, it is wonderful that you are cooking from scratch with your own garden harvest. Growing your own root vegetables and braising them in a rich beef broth is one of the most rewarding kitchen traditions.
While beef chuck roast is indeed the classic gold standard, there are several fantastic budget-friendly alternatives that develop incredible flavor and tenderness during a long, gentle braise.
Beef shank (or cross-cut shanks) is one of the best inexpensive cuts you can buy. Shank comes from the leg, which is a heavily worked muscle packed with connective tissue and collagen. As it simmers low and slow, that collagen melts down into rich gelatin, creating a velvety sauce and melt-in-your-mouth meat. Additionally, center-cut shanks include the marrow bone, which enriches your broth with deep savory flavor that pairs beautifully with garden potatoes and carrots.
Blade roast (sometimes labeled as boneless chuck blade or 7-bone roast) is another great choice. It is part of the shoulder area, often priced lower than a standard center-cut chuck roast. It has a distinctive line of connective tissue running through the middle, which completely dissolves into tenderness after three to four hours of braising.
Beef cheeks are also worth asking your butcher for. They are usually very affordable and contain an enormous amount of collagen. When braised slowly, beef cheek becomes arguably more tender and luscious than chuck roast.
One cut I would gently advise against for a long braise is bottom round (or eye of round). Round cuts come from the rear leg and are very lean. Because they lack internal marbling and connective collagen, prolonged braising tends to make them dry, tough, and stringy rather than tender and juicy.
For the best results with any of these cuts, make sure to sear the meat thoroughly on high heat before adding your liquid and root vegetables. I hope your meal turns out delicious and brings back those wonderful family memories.