Wash tomatoes. Remove peels (do this by dropping tomatoes in boiling water for 1 minute, then plunging into ice cold water). Finely chop and measure out 3.5 C.
Place chopped tomatoes into large stockpot (6-8 quart) or Dutch oven. Heat to boiling, then immediately reduce heat. Cover, simmer 10 minutes. Measure out 3 1/3 C tomatoes; return to your large pot.
Add lemon juice and basil. Combine the 1/4 C. sugar and pectin - stir into the tomato mixture. Heat to a full rolling boil, stirring constantly.
Stir in the 3 C. sugar. Return mixture to a full rolling boil; boil hard for 1 minute, stirring constantly. Remove from heat. Skim off foam with a metal spoon.
Immediately ladle jam into hot, sterilized, half pint canning jars. Allow 1/4 inch headspace per jar. Wipe jar rims and adjust lids. Process in a hot water bath for 10 minutes (start timing when water starts to boil).
Remove jars from canner; cool on counter or wire rack. As jars cool, they will seal (you will hear them "ping"). Jars may take up to 24 hours to seal - once sealed, lids will not bounce back when pushed down. Recipe makes 4 half pints