Thread the strawberries onto two skewers and brush with vegetable oil. Grill on all sides, 3 to 5 minutes total. Set aside to cool.
Pull the strawberries off the skewers; cut half into small dice (small enough to fit through a pastry tip). Stir the diced strawberries together with the strawberry jam, then add to a pastry bag fitted with a medium piping tip. Set aside.
Whip the heavy cream and powdered sugar to stiff peaks, being careful not to overwhip. Add to a second pastry bag, this one fitted with a star tip.
Slice the remaining strawberries lengthwise, either in half or quarters.
Scoop out the center of each cupcake and set aside for snacking later. Fill the cupcakes with the strawberry jam mixture and top with the whipped cream. Garnish with the sliced strawberries before serving.