Mix beef, breadcrumbs, milk, 1/2 teaspoon salt and pepper lightly in a bowl. Form 24 small meatballs about 1 inch across.
Heat oil in a deep 12-inch 5-quart saute pan over medium heat. Brown meatballs for 5 to 6 minutes, turning gently; transfer to a plate while still partly cooked.
Cook shallot and mushrooms in the same pan for 8 to 10 minutes until their moisture evaporates. Add garlic and remaining salt for 30 seconds.
Pour in broth and scrape the bottom. Add pappardelle, bring to a simmer and separate the ribbons with tongs; return meatballs and their juices.
Simmer uncovered for 9 to 12 minutes, gently lifting the noodles every 2 minutes, until pasta is tender and the centers of several meatballs reach 160°F. Add reserved water in small splashes if the noodles need more liquid.
Remove from heat. Stir Dijon and creme fraiche with a few spoonfuls of the hot sauce in a bowl, then fold this mixture gently into the pan without boiling. Serve with 6 meatballs per person.