In a large pot, cover the beans with cold water by at least 2 inches. Add herb sprigs, the whole onion half, and garlic cloves and bring to a boil over high heat. Reduce heat to simmer and cook until beans are very tender, about 1 to 2 hours. Season with salt. Drain beans, reserving bean-cooking liquid. You should have about 3 cups of cooked beans; if you have more, measure out 3 cups of beans and reserve the rest for another use. Discard herb sprigs, onion, and garlic.

In a large skillet, heat lard, bacon drippings, or oil until shimmering, or butter until foaming, over medium-high heat. Add minced onion and cook, stirring occasionally, until translucent and lightly golden, about 7 minutes. Stir in beans and cook for 2 minutes. Add ¼ cup of reserved bean-cooking liquid. Using bean masher, potato masher, or back of a wooden spoon, smash the beans to form a chunky purée; alternatively, use a stick blender to make a smoother purée. Thin with more bean cooking water until desired consistency is reached. If refried beans become too wet, simmer, stirring, until thickened; if they become too dry, add more bean-cooking liquid, 1 tablespoon at a time, as needed. Season with salt and serve.