Place potatoes in a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 15 to 20 minutes. Drain.

Meanwhile, bring a medium saucepan of water to a boil; add peas and simmer until just tender, about 6 to 7 minutes. Drain and set peas aside.

Add butter to the same saucepan; melt over medium heat. Stir in flour to make a thick paste; gradually whisk in milk, stirring constantly until slightly thickened. Season with salt and pepper to taste. Add potatoes and peas; simmer, stirring often, until potatoes are heated through, about 5 minutes. Serve immediately.