In a medium saucepan, melt the butter. When butter stops foaming, add the flour and dry mustard. Cook, stirring, for 2 minutes. Gradually add the milk, stirring until smooth. Continue cooking, whisking or stirring constantly, until the sauce has thickened. Taste and season with salt and pepper.
Coarsely chop 6 eggs and add them to the sauce mixture. Spoon over the split biscuits, English muffins, or toast and sprinkle lightly with paprika.
Slice the remaining 2 eggs, if using, and arrange a few slices on each plate.