Heat olive oil over in a 5-qt. soup pot over medium heat. Add chopped onion and garlic and season with ¼ teaspoon salt. Cook until onion is translucent, stirring frequently (approximately 2-3 minutes). **See notes below for the oil-free option.
Add diced tomatoes and their juice and cook over medium heat for 5 minutes, stirring occasionally.
Add beans and vegetable broth. Gently stir to combine.
Add rosemary sprig and bring to a boil. Once boiling, cover and reduce the heat to a simmer and cook for 15 minutes.
Use a slotted spoon or tongs to remove the rosemary sprig.
Stir in pasta and cook uncovered on medium-high until pasta is tender, stirring occasionally (approximately 8-12 minutes depending on which pasta you are using).
Once pasta is tender, turn off the heat and stir in fresh, chopped parsley.
Stir in salt and freshly ground black pepper to taste.