Heat the oven to 450°F with a rack in the upper middle position. Set out a large sheet pan and a large pot or Dutch oven.

Put the cubed eggplant and whole cherry tomatoes on the sheet pan.

Drizzle the vegetables on the sheet pan with 2 tablespoons of the olive oil and sprinkle with 1/2 teaspoon kosher salt. Toss well and spread them into a single layer so they roast instead of steam.

Roast the sheet pan for 20 to 25 minutes, until the eggplant is very tender and browned in spots and the tomatoes have burst and released juices.

Set the large pot on the stove over medium heat and add the remaining 1 tablespoon olive oil.

Add the sliced onion to the pot with a small pinch of salt. Cook for 5 to 6 minutes, stirring now and then, until the onion is soft and lightly golden at the edges.

Add the minced garlic, tomato paste, and dried oregano to the pot. Stir for 1 minute, until the tomato paste looks a shade darker and the garlic smells fragrant.

Pour the vegetable broth into the pot and scrape the bottom with a spoon to loosen any cooked bits. Raise the heat to medium-high and bring the broth to a boil.

Add the drained cannellini beans to the boiling broth. Let them cook for 5 minutes so they warm through and start to flavor the soup.

Take the sheet pan from the oven. Scrape the roasted eggplant, burst tomatoes, and all of their juices into the pot.

Stir the soup and lower the heat to a gentle simmer. Use the back of a spoon to lightly crush a few of the tomatoes against the side of the pot so they blend into the broth.

Add the rice noodles to the pot. Press them down into the hot broth as they soften and cook for 3 to 5 minutes, or until the noodles are tender but still hold their shape.