Place the bread slices on a baking sheet lined with foil and drizzle with the olive oil. Toast under the broiler on low until slightly golden and crisp.
While the bread is toasting, toss the strawberries with the sugar in a bowl to draw out the juices. They only need to macerate for about five minutes to get juicy enough.
Let the bread cool for a few minutes (so that the cheese doesn't melt when you spread it). Spread each piece of bread with a tablespoon of mascarpone cheese. Top with the strawberry slices, and then drizzle the strawberries with the balsamic vinegar.