Preheat oven to 475 F.
Cut sweet potatoes into 1/2 inch thick fries, then immerse in cold water to get rid of starch. Dry fries with clean towel and place in large bowl.
Toss fries with olive oil, salt, pepper and cayenne pepper then transfer to parchment-lined baking sheets (you will probably need one sheet per potato). Roast in the oven on the middle oven rack for 15 minutes, then flip and cook for another 12-15 minutes.
Meanwhile, while fries are cooking, make your gravy. In medium saucepan on med-high heat, add butter. Add mushrooms and onion to pan, sautéing for about 6-7 min, stirring often. Add garlic and flour, stirring well, then add vegetable broth and red wine, bringing mixture to a boil. Simmer for 10-15 min. For a creamy and smooth consistency, blend gravy using an immersion blender.
Fries should be finished around this time, so pull them out of the oven and transfer them to a pasta bowl or plate. Sprinkle with cheese curds, then ladle gravy overtop. Garnish with green onions, then serve and enjoy!