Heat 1 tablespoon of the oil in a large skillet over medium heat, when warmed, brown the sausage breaking it up as you cook.
Once the sausage is browned, add the sliced fennel and stir to coat with rendered oil. Spread the fennel out in a single layer and season with ½ teaspoon of the salt. Cover and cook, undisturbed, for 5 minutes. Remove the lid and continue cooking, stirring often, until the fennel is golden brown and tender, about 8 more minutes.
Meanwhile, bring 4 quarts of water to a boil in a large pot over high heat. Add the gnocchi and cook for 5 minutes. Drain and set aside.
Add the sliced mushrooms and the remaining 1 tablespoon oil to the skillet with the fennel. Cook, stirring occasionally, until mushrooms are tender, about 5 minutes.
Add the gnocchi, remaining ½ teaspoon salt, pepper, Chili flakes, and parsley to the skillet. Cook, stirring often, until the gnocchi is heated through and tender, 2 to 3 minutes. Remove from the heat and serve topped with reserved fennel fronds and flaky salt.
