Start water boiling in two medium-large saucepans on your stovetop. Add peas to boiling water. Don't salt, but add a pinch of sugar to the water. Cook until just tender, 3-5 minutes. Drain and set aside. Unless potatoes are really tiny, cut in half or in quarters. Cook in salted boiling water until tender, about 10 minutes (Test with a knife to be sure the are cooked through). Drain and set aside.
In a large skillet over medium heat, melt butter. Add the onion and cook, stirring, until the onion is softened. Add the flour and cook, stirring constantly, for about 1 minute. Slowly begin adding milk, stirring continuously, until well combined. Add the cooked peas and potatoes and salt and pepper. Reduce heat slightly and allow the sauce to simmer until thickened to a creamy sauce. Taste the sauce and add more salt and pepper, if needed (It should not taste flat or bland. I find I almost always need to add a bit more salt). Remove to a serving dish and serve immediately.
Notes
Be sure to read the notes above this Recipe Card for more tips on making this recipe. You'll also find step-by-step photos that you may find helpful.