Melt butter in a saucepan over medium heat. Stir in the onion; cook and stir until the onion has softened and turned translucent, about 5 minutes.
While the onions are cooking, place the diced potatoes, carrots, water and chicken soup base (or vegetable base; see Cook’s Note) in another pot and bring to a boil. Cook until vegetables are tender, about 10 minutes. Do not overcook. Season with ground black pepper to taste.
Add the flour to the cooked onions to make a paste. Cook, stirring constantly, for 2 minutes. Gradually add the milk and stir well. Cook over low heat stirring constantly until warmed through. Add the potato and carrot mixture. Stir in the parsley and thyme and heat through. Serve hot.
Substitute vegetable stock for the chicken soup base for a vegetarian version.
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