Preheat grill or barbecue. Whisk olive oil, balsamic vinegar, salt and pepper in a small bowl. Brush mushrooms, asparagus and capsicum with the mixture.
Grill or barbecue vegetables 10 cm from the heat, turning once, until tender. Allow about 10 minutes for asparagus and capsicum and about 12 minutes for mushrooms. Peel and slice capsicum when it is cool enough to handle.
Turn off grill or barbecue. Place bread on grill rack or grill until warm, about 2 minutes.
Spread bread with goat's milk cheese. Place mushrooms on each slice. Top with capsicum and asparagus. Serve warm.