Bring a large pot of salted water to a boil over high heat.
Cook the fettuccine for the time on the package, about 11 minutes, adding the broccoli for the last 3 minutes. Save a mug of pasta water, then drain.
Slice the chicken into strips and season with half the salt and the pepper.
Heat half the oil in a large skillet over medium-high heat and cook the chicken for about 6 minutes, turning, until golden and 74°C (165°F) inside.
Blend the white beans, soy milk, nutritional yeast, garlic, lemon juice, the rest of the oil and the rest of the salt until completely silky.
Lower the heat to low, pour the sauce into the pan with the chicken and warm for 2 minutes, stirring. Add the pasta and broccoli and toss with a splash of pasta water until glossy.
Finish with black pepper and chopped parsley.
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