Slice the tomatoes in half lengthwise if using cherry or grape tomatoes. Larger tomatoes can be diced small. Strain most of the liquid after dicing.
In a small skillet, heat olive oil over medium-high heat. Add garlic and stir, lightly frying for about a minute, removing before the garlic gets too brown (it can be golden.) Pour into a mixing bowl and allow to cool slightly.
Add tomatoes, balsamic vinegar, basil, and salt and pepper to the bowl. Toss to combine, then taste and add more basil or salt if needed. Cover and refrigerate for an hour or two if you have the time.
Cut the baguette into diagonal slices to allow for the most surface area possible. Melt half the butter in a large skillet and grill half the bread on both sides, making sure they're nice and buttery. Cook till golden brown on both sides. Repeat with the other half of the butter and the other half of the bread.
To serve, give the tomato mixture a final stir, then spoon generously over the slices of bread. Serve on a big platter as a first course or appetizer.