Drain and rinse two 14-ounce cans of black beans in a colander until no more foam appears. Let them drain while you prepare the pureed mixture.
Put the remaining (undrained) can of black beans and the 14.5-ounce can of diced tomatoes (including their liquid) into a food processor or blender. Add an optional pinch of ground chipotle if you want extra heat. Process about 2 minutes, until fairly smooth. Set the puree aside.
In a heavy-bottomed soup pot, heat 1 tablespoon olive oil over medium-high heat (add a little more oil if the pan looks dry). Add 1 pound lean ground beef and brown, using the back of a spatula to break it into small pieces, until no pink remains. Transfer the browned beef to a bowl and set aside.
Reduce the heat to medium-low. If the pot is dry, add a little more olive oil. Add 1/2 cup very finely diced red onion and cook, stirring, until the onion is softened but not browned, about 3–5 minutes.
Add 1 tablespoon regular chile powder, 1 tablespoon ground ancho chile pepper, about 1/4 teaspoon ground chipotle (use less if you prefer milder), and 2 teaspoons ground cumin to the softened onion. Sauté and stir for about 30 seconds, until the spices are fragrant.
Pour in 2 cups beef stock (or 1 can beef broth) and stir in 2 tablespoons tomato paste until the paste is incorporated. Return the browned ground beef to the pot and stir to combine.
Stir in the pureed bean-and-tomato mixture from step 2 and the drained, rinsed black beans from step 1. Bring the mixture to a simmer.
Reduce heat to low and simmer the chili uncovered for at least 30 minutes, stirring occasionally. You may simmer up to 2 hours on very low heat for deeper flavor. About halfway through cooking, taste and add more chile powder, ancho, cumin, or a pinch of chipotle if desired.
Just before serving, stir in 1/4 cup fresh-squeezed lime juice and cook 3–5 minutes more to blend the flavors.
Serve the chili hot.