Heat olive oil in a large pot over medium heat. Add onion, carrots, and celery and cook 6–7 minutes until softened. Add garlic and cook 2 minutes. Stir in tomato paste and cook 1 minute. Add smoked paprika, Italian seasoning, onion powder, and garlic powder and stir 30 seconds.
Pour in vegetable broth and diced tomatoes with their liquid. Add diced potato and stir to combine. Bring to a boil then reduce to a steady simmer. Cook for 10 minutes until potato is starting to soften but not yet fully cooked.
Add dry orzo directly to the simmering soup and stir. Cook for 8–10 minutes, stirring every couple of minutes to prevent sticking. Add frozen peas and corn in the last 3 minutes of cooking.
Squeeze in lemon juice and stir. Taste and adjust salt and pepper. If the soup has thickened too much, add a splash more vegetable broth and stir.
Ladle into bowls. Top with fresh parsley and grated parmesan. Serve with crusty bread alongside