In a large stockpot over medium heat, melt the butter and add the vegetable oil. Add the sliced onions and salt, stirring occasionally. Cook the onions until they are deeply caramelized, which will take about 30 minutes. The onions should reach a rich, brown color without burning. Stir frequently to prevent sticking.

Once the onions are caramelized, add the chopped garlic to the pot. Cook for an additional 2 minutes until the garlic becomes fragrant, stirring constantly to avoid burning.

Pour in the low-sodium beef broth and add the beef base. Stir well to combine. Add the ground black pepper. Bring the mixture to a simmer and let it cook over low heat for 30 to 45 minutes, allowing the flavors to meld together. Taste the soup and adjust seasoning as needed.

While the soup is simmering, preheat your oven to 325°F (163°C). Place the slices of firm bread on a baking sheet and bake for 15 minutes, or until they are golden brown and crispy. This will prevent the bread from becoming too soggy when added to the soup.

Preheat your oven's broiler. Ladle the hot soup into oven-safe bowls, leaving some space at the top. Place a slice of the toasted bread on top of each bowl of soup. Sprinkle 1 teaspoon of grated Parmesan cheese over the bread, then lay a slice of provolone cheese on top, covering the entire surface.

Place the bowls on a baking sheet and carefully transfer them to the oven. Broil until the cheese melts and starts to brown, which should take about 5 minutes. Keep a close eye to prevent burning.