1Heat olive oil and butter in a large, heavy-bottomed pot over medium-high heat. Add onion, shallots, green onions, salt, and pepper; saute until softened and beginning to brown, 4 to 6 minutes. Add garlic and herbes de Provence; saute until garlic is fragrant, about 30 seconds. Avoid burning the garlic; it will turn bitter.
2Add potatoes to onion mixture and toss well to coat. Pour in vegetable broth and milk; stir well. Cover pot and bring to a boil. Reduce heat to low and simmer, covered, until potatoes are tender and can be easily broken up with a spoon, 10 to 12 minutes.