Heat olive oil in a large pot over medium high heat.
Add onion, celery, and carrots. Cook, stirring frequently, 5-6 minutes, or until vegetables are softened and fragrant.
Stir in mushrooms and cook for an additional 3-5 minutes. Add garlic and cook 1 minute more.
Add the water, potatoes, tomato paste, Italian seasoning, paprika, and rosemary.
Bring to a boil then reduce heat to low.
Cover pot and allow to simmer, stirring occasionally, 15-20 minutes, until potatoes and carrots are fork-tender.
Stir in peas and cook, covered, an additional 3-5 minutes.
Adjust seasoning to taste and serve warm.