Add the potatoes to a large pot and pour in enough water to cover them by about 2 inches.

Bring to a boil and cook until the potatoes are fork-tender.

Reduce the heat to low, keeping the potatoes in the pot with the cooking water.

Carefully scoop out ½ cup of the hot potato water and whisk it with the flour until completely smooth.

Slowly stir the flour mixture back into the pot with the potatoes and water.

Add the milk, butter, and seasonings.

Simmer gently for about 5 minutes, stirring often, until slightly thickened.

Remove from heat and let the potatoes sit for 10 minutes to allow it to thicken even more.

Stir, taste, adjust seasoning if needed, and serve warm.