Bring a large pot of water to a boil over high heat. Boil potatoes for 15-20 minutes, or until tender. Drain.
In a medium saucepan, bring 1 cup of water to a boil. Simmer peas in boiling water for 6-7 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 about 5 minutes, stirring often. Serve immediately.