Halve the white onion; set one half aside whole and finely chop the other half. Rinse and sort the pinto beans, discarding any debris. Place the beans in a large bowl and cover with 8 cups water (for soaking). Soak 8–12 hours. For a quick soak, bring to a boil for 2 minutes, then cover and rest 1 hour.
Drain the beans and transfer to a large pot with the whole onion half and 8 cups water. Bring to a boil, skimming foam, then reduce to a gentle simmer. Cook covered 60–90 minutes until the beans are fully tender and creamy inside; add hot water only as needed to keep them submerged.
Reserve 2 cups of the bean cooking liquid, then drain the beans and discard the whole onion half.
Heat the lard in a wide skillet over medium heat until shimmering. Add the chopped onion half and cook, stirring, until translucent and sweet, 3–5 minutes. Add the garlic and cook until fragrant, about 30 seconds.
Add the beans and 1 cup of the reserved cooking liquid to the skillet. Mash with a potato masher to your desired texture, adding more reserved liquid in small splashes as needed. Fry, stirring frequently, until thick, creamy, and glossy, 8–12 minutes; the beans should hold a soft mound and sizzle at the edges.
Stir in the fine salt to taste (about 2 teaspoons). If needed, adjust consistency by frying longer to thicken or adding a spoonful of reserved liquid to loosen. Serve warm.