Put bell peppers, onion and 1/4 cup of the vinegar in a food processor. Process until very finely ground.
Scrape into a large, heavy, non-aluminum pot. Add remaining 1 1/4 cups vinegar and bring to a full boil over high heat. Reduce heat to low and simmer 5 minutes, stirring occasionally, until mixture is slightly thickened.
Stir in sugar; raise heat to high and bring to a full rolling boil, stirring constantly. Let boil 1 minute, stirring constantly. (Be careful; jam has a tendency to boil over and is very hot. Reduce heat slightly if necessary.) Remove from heat.
Stir in pectin and mix until completely blended. Skim off foam that rises to surface. Stir in TABASCO® Sauce to taste.
Ladle jam into hot sterilized jars, (1/2-pint size are ideal) leaving 1/4-inch headspace. Wipe inside and outside rims clean with a damp paper towel. Seal with sterilized new 2-piece lids, following manufacturer's instructions. Cool jars on wire rack. Store in a cool place up to 6 months. Once opened, keep refrigerated.
Makes 7 cups.
Nutritional information per one tablespoon serving: 50 Calories, 0 g protein, 10 g carbohydrates, 0 g fat, 0 mg cholesterol, 0 mg sodium