You will need 4 half-pint glass food storage jars for this sauce.
     In a large heavy saucepan, combine brown sugar and cornstarch. Stir in half-and-half, water and corn syrup.
     Cook and stir over medium heat until thick and bubbly (the mixture may look curdled at this point). Cook and stir for 2 more minutes. Remove from heat.
     Stir in butter, rum and vanilla. Let stand at room temperature for about 45 minutes until cooled.
     Divide the sauce between the 4 jars. Seal and decorate with pretty fabric rounds tied to the lids with ribbon (or however you wish to decorate the jars). Attach a card with directions for reheating the sauce. The jars can be stored in the refrigerator for up to 1 week.
     To reheat the sauce, empty the contents of one jar into a small saucepan. Heat over low heat just until warm. Serve the warm sauce over cake, ice cream, fruit, etc.
     Each jar contains about 1 cup of sauce. Makes 4 jars.