Place the cashews in a small pot, cover with water by 2 inches, and boil for 10 minutes until very soft. Drain and set aside.
Slice the chicken breasts in half horizontally so they cook evenly, then season with salt, black pepper, and Italian seasoning. Heat the olive oil in a large skillet over medium-high heat and cook the chicken for 5-6 minutes per side until golden and it reaches 165°F.Transfer the chicken to a cutting board, rest for 5 minutes, then slice into strips.
Bring a large pot of salted water to a boil and cook the fettuccine according to package directions, adding the broccoli florets during the last 3 minutes. Reserve 1 cup of the pasta water, then drain.
Lower the skillet heat to medium, melt the dairy free butter, and sauté the garlic for 1 minute until fragrant but not browned.
Add the softened cashews, garlic butter, almond milk, chicken broth, nutritional yeast, lemon juice, miso paste, salt, and nutmeg to a blender. Blend on high for 1-2 minutes until completely silky and smooth.
Pour the sauce back into the skillet and simmer over medium-low heat for 2-3 minutes until it thickens slightly. Add the pasta and broccoli and toss to coat, splashing in reserved pasta water as needed to make it glossy.
Top with the sliced chicken, sprinkle with parsley and extra black pepper, and serve right away.