In a Dutch oven, combine the strawberries and butter. Stir in the pectin. Bring the mixture to a full rolling boil over high heat, stirring constantly. Stir in the sugar; return to a full rolling boil. Boil and stir for 1 minute. Immediately stir in the basil.
Remove from the heat and skim off the foam. Ladle the hot mixture into nine hot half-pint jars, leaving ¼-inch of headspace. Remove air bubbles and adjust the headspace, if necessary, by adding more hot jam. Wipe the rims. Center the lids on the jars; screw on the bands until fingertip tight.
Place the jars into a canner with simmering water, ensuring that they are completely covered with water. Bring to a boil; process for 10 minutes. Remove the jars and cool.
