Set an oven rack about 6 inches from the broiler and heat the broiler to high. Put a large soup pot on the stove over medium heat.

Add the olive oil and butter to the pot. When the butter melts, add the sliced onions and a pinch of salt.

Stir the onions to coat them well. Cook for 8 minutes, stirring every 1 to 2 minutes, until they soften and start to turn light gold.

Lower the heat to medium-low. Cook the onions for 12 to 15 minutes more, stirring often, until they are deep brown and very soft; if the pot starts to dry out, add 1 tablespoon water to keep them from scorching.

Add the sliced mushrooms to the pot. Cook for 6 to 8 minutes, stirring now and then, until the mushrooms give off their liquid and that liquid cooks away.

Add the chopped garlic to the pot. Stir for 30 seconds, just until it smells fragrant.

Pour the vegetable broth and soy sauce into the pot. Stir along the bottom of the pot to loosen any browned bits stuck there.

Raise the heat to medium-high and bring the soup to a gentle boil. Lower the heat so the broth stays at a steady simmer.

Simmer the soup for 8 minutes so the onion and mushroom flavor can blend into the broth.

While the soup simmers, put the baguette slices on a sheet pan. Broil for 1 to 2 minutes, until the tops are lightly toasted.

Turn the baguette slices over on the sheet pan. Divide the grated Gruyere over the bread and broil for 1 to 2 minutes more, until the cheese melts and bubbles at the edges.

Bring the soup back to a gentle boil. Add the rice noodles to the pot and press them down so they are covered with broth.