Warm a teaspoon or two of olive oil in a large, heavy pot (at least 5 quarts) over medium-high heat.
Add the onion and cook until just starting to turn golden brown, 5 to 8 minutes. Add the potatoes and ΒΌ tsp. salt, and cook until the edges of the potatoes are beginning to soften, about 5 minutes.
Push the potatoes to the side of the pan, clearing a space in the middle. Add the garlic, oregano and chili flakes to the middle of the pan. Cook until you can smell the garlic, about 30 seconds, then stir everything together with the onions and potatoes.
Add the corn, peas, cheese and milk to the soup. Bring back to a simmer (just a few bubbles, not a rolling boil) and cook until the corn and peas are cooked through, about 5 minutes. Taste and add salt and pepper as needed.