Heat the vegetable oil in a large skillet over medium heat. Once it begins to shimmer, add the shallot and cook for 2 minutes.
Add the fennel and cook for 3 to 5 minutes, until it has softened.
Toss in the garlic and cook for about 30 seconds.
Pour in the white wine and stir, breaking up any bits on the bottom of the pan. Add the wild rice and the parmesan cheese rinds and stir until coated and mixed well.
Pour the vegetable broth in along with the salt and bring to a boil. Cover, reduce heat to low, and cook for 45 minutes + another 40 minutes if you desire softer rice.
Turn off the heat and let the rice sit covered for 10 minutes while you prepare the dressing.
Transfer the rice to a large serving bowl and drizzle with the dressing, mixing well. Mix in finely chopped reserved fennel fronds or any other mixings* you would like.