Puree the strawberry jam in a blender or mini food processor so that it is smooth, with no chunks of berries.
Line a 8” x 8” baking pan with parchment paper, and grease the paper, including up the sides.
Stir the sugar, chocolate, half and half, corn syrup, jam and 1 tablespoon of the butter in a medium saucepan over medium heat until the chocolate is completely melted.
Cover the pan and reduce the heat to medium-low. Bring to a boil, which should take 2-3 minutes.
Uncover the pan and clip a candy thermometer to the pan so that it isn’t touching the bottom or sides of the hot pan. Cook without stirring until the temperature reads 235°F.
Turn off the heat and add the rest of the butter. DO NOT STIR or otherwise disturb the fudge.
Allow to cool to 125°F, which should take 35-50 minutes.
Use a wooden spoon to stir in the vanilla, and beat until the fudge is thick and beginning to lose its gloss. Immediately pour into the prepared baking pan to cool completely. Cut into 1” pieces and store in an airtight container at room temperature.