Start the soup: Set a large pot on the stove over medium heat. Add the olive oil and let it warm for about 30 seconds.

Add the chopped onion and sliced carrot to the pot. Cook, stirring now and then, for 5 minutes, until the onion looks soft and the carrot has started to soften at the edges.

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

Put the drained roasted red peppers into the pot. Stir them with the onion and carrot for 2 minutes to warm them through.

Build the broth: Add the drained cannellini beans and the vegetable broth to the pot. Stir well to combine.

Raise the heat to medium-high and bring the soup to a gentle simmer. Small bubbles should break around the edges of the pot.

Lower the heat to medium and simmer for 8 minutes, until the carrot slices are fully tender when pierced with a fork.

Blend the base: Turn off the heat. Use an immersion blender right in the pot to blend the soup until smooth, or carefully transfer the hot soup to a blender, blend with the lid vented, and pour it back into the pot.

Put the pot back over medium heat. Bring the blended soup back to a gentle simmer.

Cook the noodles: Add the rice noodles to the pot. Press them down into the broth with a spoon so they start to soften.

Cook the noodles for 3 to 4 minutes, stirring once or twice, until they are tender but still hold their shape.

Add the baby spinach to the pot. Stir it into the hot soup so it starts to collapse.