Heat the oil in a large pot over medium-high heat, then add the diced onion, sliced carrots, and celery. Sauté for 4 to 5 minutes until softened, stirring frequently to avoid burning. Add minced garlic, Italian seasoning, kosher salt, and black pepper, then sauté for another 30 seconds until fragrant.
Incorporate the diced Yukon gold potatoes, chopped green beans, canned diced tomatoes along with their juices, bay leaves, and vegetable broth into the pot. Stir everything together thoroughly before bringing it to a boil over high heat.
Once boiling, reduce heat to low and cover the pot with a lid, allowing it to simmer gently for about 20 minutes or until potatoes are just fork-tender.
Stir in the frozen corn and peas into the simmering soup mixture, cooking for an additional 5 to 7 minutes until heated through.
Turn off the heat once everything is cooked through; stir in fresh lemon juice and chopped parsley right before serving for brightness and flavor enhancement. Ladle generous portions into bowls and enjoy!