Special equipment: four 12-inch skewers
Prepare a grill for medium-high heat. Toss the cake, strawberries and 1 1/2 cups sugar in a large bowl until the cake and berries are coated well on all sides with sugar (they can be a little lumpy and unevenly coated). Thread a piece of cake and a strawberry onto a skewer; repeat 3 times on the skewer. Repeat with the remaining skewers and ingredients. Set the skewers on a rimmed baking sheet.
Whisk together the cream, the remaining 2 tablespoons sugar and the vanilla in a medium bowl. Beat with a hand or stand mixer until soft peaks form. Cover and refrigerate.
Lightly oil the grill grates. Put the skewers on the grill, and grill, covered, until they are lightly marked, about 1 minute. Use a spatula to gently loosen them, and use tongs to flip them over. Continue to grill, covered, until the cake and strawberries are toasted with grill marks and the sugar starts to bubble and harden, 2 to 3 minutes. Serve with the whipped cream on the side.
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