Preheat the oven to 400°F and line two baking sheets with parchment paper.
Arrange the baguette slices in a single layer on the baking sheets and drizzle both sides with olive oil. Bake for 10 to 12 minutes, or until golden and toasted.
Meanwhile, in a large bowl, stir together the tomatoes, basil, garlic, balsamic vinegar, salt, and several grinds of pepper. Season to taste.
Remove the bread from the oven. Use a slotted spoon to scoop the tomato mixture onto the bread pieces, leaving behind any excess juices. Drizzle with olive oil and sprinkle with flaky sea salt. Serve immediately.