Add the gnocchi and cook for 3-4 minutes until they float and are tender. Drain, rinse, and drizzle with extra virgin olive oil and a sprinkle of salt. Set aside.
Prepare the Aromatics:
As you wait for the water to boil, heat the cooking oil in a wide pot over medium heat. Once hot, add the diced onion and cook, stirring often, for 5-6 minutes until softened and beginning to brown. Add the garlic and cook for 1 minute or until fragrant, being careful not to burn it.
Melt the butter into the onions. Once melted and frothy, add the mushrooms and cook, stirring often, until they turn a deep golden brown and crisp up around the edges, about 10 minutes. Season with salt, pepper, and crushed red pepper.
Finish the Parmesan Broth:
Pour in the chicken stock and scrape up any fond stuck to the bottom. Add the parmesan rinds and season again to your preferences. Bring to a boil and then reduce heat and simmer for 25 minutes or until the broth has reduced a bit and the parmesan rinds are very soft.
Add Gnocchi and Broccolini:
Remove and discard the parmesan rinds. Bring the broth back to a very low boil and then add the broccolini and cook for 1 minute. Reduce heat and add the cooked gnocchi and simmer for 2 minutes or until the broccolini is bright green. Stir in the lemon juice and turn off the heat.
To Serve:
Divide the gnocchi and broth between bowls and garnish with extra virgin olive oil, fresh parsley, and more shredded parmesan cheese, if desired. Enjoy!