Bring a large pot of water to a boil, then salt the water. The rule of thumb is to add about 1 teaspoon of table salt for every quart of water. You need enough water to cover the potatoes, so it will probably be around 8-12 cups of water, so 2-3 teaspoons of table salt will be needed to season the water.

Add the potatoes and cook for 10-15 minutes, just until the potatoes are fork tender and can be easily pierced but aren't falling apart. Remove the potatoes with a slotted spoon and set to the side.

Cook the peas in the same water as the potatoes for 2-5 minutes until tender, but do not overcook. They should be bright green and still have some texture to them. If using frozen peas, there is no need to cook them at this point. Instead, wait to add them with the cooked potatoes to the sauce, then simmer until warm. Drain the water and add the peas to the potatoes. Set aside.

In the same pot, melt the butter then sprinkle with the flour. Whisk until the flour has absorbed the butter, about 1 minute.

Whisk in the milk, then season with the salt and pepper and cook until slightly thickened. Add the peas and potatoes, stirring to coat in the sauce, and simmer until warmed through. If the sauce gets too thick, thin it out with some additional milk. If it isn't thick enough, you can whisk more flour in to a little additional milk and stir that into the sauce to help thicken it.

Taste and adjust the salt and pepper as needed. Serve immediately.