Pour the oil into a saucepan. Add the butter and melt over medium-high heat.
Once the butter has melted, add the onions and cook for 20 to 25 minutes, stirring from time to time until the onions are nicely browned. Drain and set aside.
Shape 12 small balls of goat cheese. Set aside.
Place the slices of baguette on a baking sheet and grill for 1 to 2 minutes.
Let the croutons cool.
Top each crouton with the caramelized onions.
Place a cheese ball on top of the onions and a walnut half on top of the cheese.