Preheat oven to 375 degrees. Arrange baguette slices in a single layer on a baking sheet and toast in the oven for 5 minutes. Turn slices over and using a pastry brush, brush each slice lightly with vegetable oil. Sprinkle each slice with ¼ teaspoon sugar. Return baking sheet to oven and toast an additional 5 to 10 minutes until lightly brown. Let cool completely.
Wash and finely dice strawberries. In a large bowl, combine strawberries with mint and 2 tablespoons of sugar and let stand at room temperature about 30 minutes or until syrupy.
Top each baguette slice with a heaping tablespoon of the strawberry mixture and pour any additional syrup over the slices. Serve immediately.