Brown ground beef in a large soup pot over medium-high heat, breaking up with a wooden spoon, until no longer pink. Drain and return to pot.
Meanwhile, melt butter in a small saucepan over medium heat then whisk in flour and cook for one minute. Slowly whisk in 1 cup milk and bring to a simmer. Reduce heat and simmer an additional 3-4 minutes. Remove from heat then stir in shredded cheese until smooth. Set aside.
Add taco seasoning, Rotel, black beans, and remaining 1½ cups milk into cooked ground beef then stir well to combine. Bring to a heavy simmer then turn heat down to medium and simmer for 10 minutes, stirring occasionally. Serve hot.