Place the tomatoes in a kettle. Bring to a boil, reduce the heat, cover, and simmer for 10 minutes. Add the lemon juice and basil. In a small bowl, combine ¼ cup of the sugar and pectin and add to the tomatoes. Heat to a full rolling boil, stirring constantly. Add the remaining 2-¾ cups sugar. Return to a rolling boil and cook for 1 minute, stirring constantly. Remove from the heat and skim off the foam. Ladle the jam into hot, sterilized ½-pint canning jars, leaving a ¼-inch headspace. Seal with lids and process in a boiling-water bath for 5 minutes.