In a large skillet over medium heat, melt 2 tablespoons of butter along with 2 tablespoons of olive oil.
Add the sliced onions in an even layer to the skillet along with salt, pepper, and thyme sprigs.
Cook, stirring only occasionally, while the onions brown and caramelize for about 15 minutes.
Add 2 teaspoons sugar to the onions, stir, and add ¼ cup of beef broth (or stock). Stir and cook for an additional 5-10 minutes until deeply caramelized.
Remove the onions from the heat, and dispose of the thyme stems.
The caramelized onions are now ready to use or store in an air-tight container in the refrigerator.
To make the garlic toasts:
Preheat oven to 425-degrees Fahrenheit.
Use a serrated knife to slice the bread into 1" diagonal slices.
Place the slices on a parchment-lined baking sheet, brush them with olive oil, and season each with salt and pepper.
Bake in the preheated oven for 15 minutes until lightly golden.
Meanwhile, remove the skins from 2-3 garlic cloves.
When the toasts cooled, rub the raw garlic cloves lightly over each toasted crostini.
How to assemble the French onion crostini appetizers:
Once the onions are cooled, and the toasts have been rubbed with garlic, it's time to assemble the appetizers.
Spread approximately 1 tablespoon of the caramelized onions evenly onto each garlic toast.
Top each with some shredded Gruyere cheese and heat in a 350-degree (F) oven until the cheese has melted (approximately 10 minutes).
Before serving, top each with a small sprig of fresh thyme and serve warm or at room temperature.
Notes
The caramelized onions for this recipe may be made in advance and store in an air-tight container in the refrigerator for up to 3 days if needed.