Cut the potatoes into ½ inch batons, pat them completely dry, and set aside to remove excess moisture.
Toss potatoes with oil, seasonings, and roast at 450°F for 25 to 35 minutes, flipping once, until golden and crisp.
Melt butter in a skillet over medium heat and cook mushrooms for 8 minutes until deeply browned.
Add garlic and shallot, stir in flour, then pour in wine, broth, cream, and seasonings, simmering about 5 minutes until thick.
Fry eggs in butter or oil over medium heat until whites are set and yolks stay runny.
Plate fries, spoon mushroom sauce over top, add a fried egg, garnish as desired, and serve hot.