Combine the oil, onions, and jalapeŇos in a large heavy stockpot over high heat. SautČ for 2 to 3 minutes, or until slightly soft. Add the garlic, pepper, anchovy fillets, cloves, salt, lemons, corn syrup, cane syrup, vinegar, water, and horseradish and bring to a boil. Reduce the heat and simmer, stirring occasionally, for about 6 hours, or until the mixture barely coats a wooden spoon. Strain.
Spoon the hot mixture into 3 hot sterilized pint-size jars, filling to within 1/2 inch of the top. With a clean damp towel, wipe the rim and fit with a hot lid. Tightly screw on the metal ring. Process in a hot-water bath for 15 minutes.
Using tongs, remove the jars, place on a towel, and let cool. Test the seals. Tighten the rings. Store in a cool, dark place. Let age for at least 2 weeks before using. Can be stored in the refrigerator in a covered jar or bottle indefinitely. Refrigerate after opening.
Yield: 6 cups or 3 pints