Brown ground beef in a large soup pot over medium-high heat, seasoning with salt and pepper, 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, season with salt and pepper, then switch to a wooden spoon and stir mixture until thickened, about 3-4 minutes. Remove from heat then stir in shredded cheese until smooth. Set aside.
Add taco seasoning, rotel, black beans, cheese sauce, and remaining 1-1/2 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 with crushed tortilla chips and more shredded cheese, if desired.
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