Heat oil in a large skillet over medium-high. Add garlic and crushed red pepper; cook, stirring often, until fragrant, about 1 minute. Stir in beans, broth, yeast, lemon zest and juice, and salt. Bring to a boil, and remove from heat. Pour bean mixture into a blender. Secure lid to blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process until smooth. Transfer bean mixture back to skillet.
Bring a large pot of salted water to a boil over high. Add fettucine to water, and boil, stirring often, until al dente, about 10 minutes. Drain, reserving 1 to 1 ½ cups cooking water. Add pasta to skillet with bean mixture; toss to coat, adding reserved cooking water as needed to thin sauce. Add spinach; cook, stirring until just wilted, about 2 minutes.
Divide pasta among 4 bowls. Sprinkle with parsley and red pepper.
