Cook the Beans: In a large pot, combine the rinsed pinto beans, the roughly chopped 1/4 onion, and 5 cups (1200 ml) of water.
Bring to a boil, then reduce the heat to a low simmer.
Cover and cook for 2. 5 to 3 hours, or until the beans are very tender. Skim any foam from the surface occasionally and add more water if needed to keep the beans covered in broth.
Sauté Aromatics: In a large, heavy-bottomed skillet (cast iron is ideal), heat the 6 tablespoons (90 ml / 3 fl oz) of olive oil over medium heat.
Add the 1/2 cup (480 ml) of finely chopped white onion and cook until translucent and soft, about 5-7 minutes.
Fry and Mash: Add about 1 cup (240 ml) of the cooked beans along with some of their broth to the skillet with the onions.
Using a potato masher or the back of a wooden spoon, begin mashing the beans directly in the pan.
Thicken the Beans: Continue adding the beans and broth, one cup at a time, mashing continuously. Increase the heat to medium-high and stir constantly as the mixture thickens.
Cook until the beans have dried out, sizzle around the edges, and begin to pull away from the sides of the pan.
Serve: Once the beans are thick and creamy, season with the 1/2 teaspoon (10 ml / 0.3 fl oz) of salt, or more to your taste.
Serve warm, garnished with your favorite toppings.
Add a bay leaf or a couple of peeled garlic cloves to the pot while the beans are simmering for an extra layer of aromatic flavor.