In a large skillet, heat the olive oil over medium heat. Add the sunchokes and season with salt and pepper. Cook in a thin layer until both sides are browned, about 2 minutes per side. Remove from the skillet and drain on a paper towel.
Meanwhile, bring a large pot of salted water to a boil. Prepare the pasta according to the instructions on the package, cooking until al dente. Drain the pasta.
Wipe any excess oil from the skillet and drizzle enough olive oil to lightly coat the bottom of the pan. Add the shallot and cook until soft, about 2 minutes. Add the garlic, broccoli rabe, and lemon juice. Season with salt and pepper. Toss until the broccoli rabe wilts, about 2 minutes. Add the cooked pasta, sunchokes, lemon zest, feta cheese, pine nuts, red pepper flakes, and a grating of the pecorino cheese, if desired. Taste and adjust the seasonings.