Place dry mustard in a bowl, add vinegar and rum. Do not stir. Cover and let stand 5 - 12 hours.
Place mustard mixture in the top of double boiler, or in a bowl set on top of an inverted bowl in bottom of big pot with water half way up bottom one (my home made double boiler). Water should be hot but not boiling.
Add eggs one at a time, whisking completely after each.
Gradually whisk in sugar until smooth, beat in butter, salt and pepper and cook until thick, about 5 minutes.
*DO NOT OVERCOOK OR EGGS WILL CURDLE*.
spoon into sterilized jars and seal. Store in refridgerator until ready to use.