Gather all the ingredients together. This dish cooks rather quickly. If you have kids, enlist them to start toasting the English Muffins or bread! Prepare your beef by pulling it apart into shreds.
Melt the butter in a deep sided non-stick pan. When it begins to get bubbly, add the flour, and continue to stir until the flour is dissolved. Add the dried beef and sautee on low to moderate heat until it begins to darken (about 5-8 minutes).
Add the milk, and increase to heat to moderate. Cook until it begins to steam, then add the cheese all at once. At this point, you are "get your hands washed, phones off, 5 minutes to eat.."
Add the paprika and the ground black pepper as the cheese melts, but keep stirring. The sauce will thicken and become rich. Take it off the heat, and either put the whole saucepan on the table or pur it in a large bowl. Serve immediately, it thickens more as it cools! Enjoy!