Melt butter in a medium saucepan. Stir in flour. Let it heat over a medium heat, but don't let it brown. Stir in milk, blending well. When it starts bubbling around the edges, add the beets, salt, and pepper. Reduce heat to very low and simmer, covered, for 5 minutes.
NOTE: You can also add a dash of nutmeg and 1/2 cup of plain yogurt, after reducing the heat to low.