Heat a dash of oil in a saucepan, and add the sliced red onion and minced garlic. Cook over a fairly low heat until the onion is cooked to your liking - cooking it for longer will result in a softer, sweeter mixture, so I'd recommend leaving it at least 15 minutes, stirring regularly.
When the onions are cooked, add the balsamic vinegar and blackberries, and cook for a further 5 minutes, until the blackberries have cooked down. Set aside to cool.
In a bowl, combine the crumbled goat's cheese and chopped basil with a pinch of salt and pepper. Mix well. You can add a dash of extra virgin olive oil to loosen it up if needed.
Cut the baguette into thick slices (I like to cut on a slight diagonal to give larger pieces). Brush both sides of each slice lightly with olive oil, and place under a medium grill (broiler) for a few minutes each side until golden brown and crispy.
Allow the toasted bread to cool for a minute or two, then spread with the basil and goat's cheese mixture. Just before serving, top with a spoonful of the balsamic blackberry compote, and a few more fresh basil leaves if desired. Best served at room temperature.