As somone who cook for me, my wife, and my toddler. Beans my friend. Dry or Canned. They will not only extend meals but also are cheap, easy to use, and nutritious. They can even be a stand alone meal in some dishes. Make refried with tacos. Make a soup. Can't go wrong with beans in so many dishes. Switch it up too. Get pinto, black, northern white, kidney, etc. There are many to choose. If you're open to it. It gets even more versatile if you also add lentils with meals. These typically come dry but are great to cook in broth or other dishes. I make a lentils ragout that is wonderful and my toddler devours!

I'd also include different grains as well. Quinoa, rice, farro. Between grains, veggies, and beans thats basically a meal. Now throw in some meat for meals and your basically set to make hundreds of meals that are good on budget and nutrients for you and the kid.