In a large pot of salted boiling water, cook the potatoes until very tender, about 25 minutes. Drain well.
Return the potatoes to the pot. Add butter and mash the potatoes until almost smooth. Mix in milk and Dijon mustard. Add more milk, if needed to make them nice and creamy. Season to taste with salt and pepper.
Notes
*If you are preparing this recipe as GLUTEN-FREE, just be sure to use a brand of Dijon that is known to be GF.