Brush the baguette slices on both sides with 2 tablespoons of the olive oil. Place the slices on a rimmed baking sheet and sprinkle with 1/2 teaspoon salt. Bake for 10 minutes, rotating the baking sheet halfway through.
In a medium bowl, combine the vinegar, honey, 1/2 teaspoon salt and the remaining 2 tablespoons olive oil; whisk until smooth and emulsified. Add the cherry tomatoes, strawberries and basil to the dressing; mix well to coat. Allow to sit at room temperature for 10 minutes to let the flavors marry.
Drain the burrata and dry carefully. Using a fork, tear the burrata into small pieces. Place some burrata on each toast, being sure to get a little of the creamy center on each piece. Top with some of the tomato-strawberry mixture and drizzle with a touch of dressing.