Bring a large pot to boil and boil the potatoes for 10-12 minutes or until fork tender.: The kitchen will start to smell faintly of warm starch as the water simmers, and you should hear a gentle, rolling boil. Test with a fork for resistance, aiming for tender but intact pieces that yield without disintegrating, because overcooked potatoes can turn mushy and absorb too much sauce. To avoid uneven cooking, cut the potatoes into similar sized pieces and watch that the boil remains steady not violent, which causes chipping and rough edges.
Add the peas the last 3 minutes of cooking time. Drain.: When the timing nears, slide in the peas , and you will notice the pot brightening as the green color blooms. The short cooking keeps the peas sweet and slightly firm, which contrasts with the soft potatoes . A common mistake is overcooking the peas until they turn dull and mealy, so set a timer and avoid letting them sit in hot water after draining.
In a large saucepan over medium high heat add the butter and melt. Whisk in the flour, salt and pepper until it thickens up.: Steam escapes as you pour, and the potatoes and peas will glisten slightly when properly drained. Removing excess water prevents a watery sauce that cannot cling to the ingredients. If you rush this step and leave too much water, the sauce will be thin and the dish may separate, so let them drain fully, and if needed return briefly to the pot on low heat to evaporate lingering moisture.
Whisk in the milk, heavy cream, and parmesan over medium high heat until thick.: The butter will foam and then settle, releasing a warm, buttery aroma. Maintaining medium high heat helps the butter melt quickly without browning, which preserves a clean flavor for the roux. A typical error is letting the butter brown, which introduces an unintended nutty note and can overpower the delicate peas , so watch it closely and reduce heat if it starts to color.
Add the potatoes and peas back to the sauce for 2-3 minutes and serve.: As you whisk the flour into the melted butter , the mixture will turn from glossy to slightly matte and smell of cooked starch, signaling the roux is ready. Cook briefly so the raw flour taste disappears, but do not let it darken. If lumps form, keep whisking patiently and consider lowering the heat; persistent lumps can create a grainy sauce, while a smooth roux ensures a silky finish.
Whisk in the milk, heavy cream, and parmesan over medium high heat until thick: When you add the milk and heavy cream in a slow steady stream while whisking, the sauce will emulsify and become glossy. The aroma becomes rich and slightly sweet as the dairy warms, and the parmesan melts in to lend a savory depth. Simmer gently so the sauce reduces and coats the back of a spoon; boiling aggressively risks breaking the sauce or curdling. If the sauce seems thin at first, be patient and simmer to concentrate flavors and reach the proper consistency.
Add the potatoes and peas back to the sauce for 2 to 3 minutes and serve: Once combined, you'll see the sauce cling to each piece of potato and pop of pea , creating a glossy, comforting presentation. Heat them just long enough for flavors to marry without softening the peas further, and stir gently to avoid smashing the potatoes . Overstirring or cooking too long can break textures, so aim for 2 to 3 minutes of gentle warming, then transfer to plates and enjoy immediately while the sauce is warm and silky.