Heat up half a tablespoon of oil in a large pot on medium heat. Once the oil is hot, add the minced garlic and diced onion pieces. Cook until the onion pieces are soft and translucent. (If the pot contents are starting to look very dry and stick to the bottom of the pot, you can turn down the stove heat setting slightly and add a little bit of vegetable broth or water into the pot.)
Uncover the pot, stir the contents then add in the salt and ground black pepper. Stir until combined. Taste a green bean or two to see if you need to cook it longer and also to adjust the seasonings if needed. If the green beans are not cooked through yet, cover the pot and let the contents simmer a few minutes longer (you can add in a bit of water or vegetable broth if needed to keep the pot contents from drying out).
For an oil-free recipe, simply use 2-4 tablespoons of vegetable broth in a heated skillet to sauté the onion and garlic pieces (until the onion pieces are soft and translucent), instead of using vegetable oil.