Gather all your ingredients to make the cooking process smoother.
Prepare the vegetables by dicing the onion, carrots, and celery, and mincing the garlic. Peel and cube the potatoes.
In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5. Then stir in the garlic, carrots, and celery, cooking for another 5.
Add the cubed potatoes, thyme, parsley, and black pepper. Pour in the broth and bring to a boil. Reduce heat and let simmer for 15-20.
Once the potatoes are tender, add the corn and peas, cooking for an additional 5. Then add the milk and cheese, stirring until melted.
Serve the soup hot, adjusting seasoning with salt if needed.