Cut off the fennel stems. Halve lengthwise; cut out and discard the core then dice the bulb. (We searched this on YouTube and found a good video on how to prepare fennel.)
Cook the pasta according to package directions, reserving ½ cup of cooking water. Set aside.
While the pasta cooks, heat 2 tablespoons of olive oil on medium-high. Working in batches if necessary, add the spinach. Cook, stirring occasionally, 2-3 minutes, until wilted. Transfer to a strainer; rest strainer over a bowl. Using a spoon, press down on the cooked spinach to release as much liquid as possible. Discard the liquid. Transfer drained spinach to a cutting board; finely chop. Wipe out the pan.
While the pasta continues to cook, in the pan used to cook the spinach, heat 2 tablespoons olive oil on medium-high heat. Add the mushrooms and cook, stirring occasionally, 8-10 minutes or until browned and crispy. Transfer to a paper towel-lined plate, leaving any browned bits in the pan. DO NOT WIPE THE PAN.
Add 2 teaspoons of olive oil to the same pan, heat on medium-high heat. Add the fennel. Cook, stirring occasionally, 2-4 minutes or until lightly browned and softened. Add the garlic. Cook, stirring frequently, 1-2 additional minutes or until fragrant.
To the garlic and fennel, add the cooked pasta, chopped spinach, butter, lemon zest, the juice of all 4 lemon quarters, and half the reserved pasta cooking water.
Cook, stirring vigorously, 1-2 minutes or until thoroughly combined. (If the sauce seems dry, gradually add the remaining pasta cooking water to achieve your desired consistency.) Season with salt and pepper to taste.
Divide the finished pasta between 2 dishes, top with mushrooms, cheese, chervil, and fennel pollen.