Warm the olive oil in a small skillet over medium-low heat. Add the minced garlic and sauté for roughly one minute, just until the garlic starts to take on a golden hue—avoid browning. Transfer this infused oil to a large bowl and allow it to cool slightly.
Remove the cores from the roma tomatoes and dice them finely. Drain the excess liquid using a colander, then blot the tomatoes with paper towels to remove residual moisture. Add the dried tomato pieces to the bowl with the garlic oil.
Arrange the basil leaves in a stack, roll them into a tight cylinder, and slice into thin ribbons using a sharp knife. Incorporate the chiffonaded basil into the tomato mixture.
Introduce one tablespoon of balsamic vinegar along with the salt and pepper. Stir the mixture gently to combine and allow it to marinate in the refrigerator for 30 minutes.
Preheat the oven to 400°F, positioning a rack in the center. Line a baking sheet with parchment paper and arrange the baguette slices on top. Brush each piece lightly with olive oil. Bake for 5 minutes, then switch to broil and toast for an additional 1–2 minutes, watching closely to prevent burning.
Remove the toasted slices and spread each with a layer of goat cheese. Spoon the tomato mixture on top and finish with a drizzle of balsamic glaze before serving.