Bring a large pot of water to a boil over high heat. Boil potatoes for 15 to 20 minutes, or until tender.
Drain.
In a medium saucepan, bring 1 cup water to a boil. Simmer peas in boiling water for 6 to 7 minutes, or until tender (do NOT overcook).
Drain.
Using the same saucepan, melt butter 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. Now add potatoes and peas to the sauce; simmer for about 5 minutes, stirring often.