Bring a large pot of salted water to a rolling boil, then add the farfalle and cook according to package directions until al dente (usually 9-11 minutes). While the pasta cooks, slice the mushrooms into 1/4-inch thick pieces, smash and finely mince the garlic cloves, and roughly chop the parsley. Drain the cooked pasta thoroughly but do not rinse it—the starch helps the final salad hold together better. Set the cooked pasta aside in a large mixing bowl.
Heat 3 tablespoons of olive oil in a large skillet over medium-high heat. Add the sliced mushrooms and red pepper flakes, cooking undisturbed for 2-3 minutes to develop a golden crust, then stir and cook another 2 minutes until the mushrooms are tender and lightly browned. Reduce heat to medium, then add the minced garlic and pine nuts, stirring constantly for about 1 minute until fragrant and the pine nuts are lightly toasted. Sprinkle in the paprika and oregano, stirring for 30 seconds to bloom the spices and release their oils—this step is crucial for maximum flavor.
Add the edamame and vegan butter to the skillet, stirring gently for about 1 minute until the butter melts and the edamame is heated through. Stir in the chopped parsley, then add the baby spinach in handfuls, stirring gently as it wilts—this should take about 3-4 minutes total. The spinach will reduce significantly, so don't worry if it seems like a lot at first. Once the spinach is fully wilted and the mixture is heated through, pour the entire contents of the skillet into the bowl with the cooked pasta.
Toss the pasta mixture gently but thoroughly to combine all ingredients evenly. Drizzle in the lemon juice and season with the black pepper and vegan parmesan, tossing again until everything is well coated. Taste as you go—I find that the lemon juice brightens the earthiness of the mushrooms and spinach beautifully, so don't be shy with it. Serve the salad warm or at room temperature, as preferred.