In a medium saucepan over medium heat, warm olive oil until shimmering. Add the finely chopped onions and salt. Cook, stirring periodically until the onions are softened and translucent. This will take about 5 minutes.
Add garlic, chilli powder and ground cumin. Stir together with onions until fragrant (about 30 seconds to a minute). Add the black beans and water to the saucepan. Stir together, cover the pan and allow to cook for 5 minutes.
Reduce heat to low and remove saucepan lid. Use the back of a fork or potato masher to mash saucepan ingredients together until at least half of the black beans are mashed and you've reached your desired consistency. Continue to cook on low, stirring frequently, for 3-5 more minutes.
Turn off the stove, remove saucepan from heat and stir in chopped fresh cilantro and lime juice. If necessary, add more salt, cilantro or lime to taste. If your refried beans appear dry, add small splashes of water and stir to combine until no longer dry. Cover bean mixture until you're ready to serve.