Make the cashew cream: Soak the cashews in water for 2 hours, or pour boiling water over them, cover, and let soak for about 20 minutes. Drain. Put the cashews in a blender with the water and blend on high for 30 seconds or longer, until smooth. Set aside.
Make the pasta: Cook the pasta in a saucepan according to package directions. When done, drain the pasta.
Cook the broccoli: While the pasta is cooking, cook the broccoli and garlic in a Dutch oven or other large pot, covered, with several tablespoons of water, for 3–4 minutes, until tender.
Complete the dish: Add the cashew cream, arugula, tomatoes, lemon zest and juice, salt, and pepper to the broccoli and garlic. Stir together and cook a few minutes more until the cream is thickened and the arugula has wilted. Add water if needed.
Combine with pasta: Add the cooked pasta to the sauce, toss together, and transfer to a serving dish or dishes. Serve with vegan Parmesan sprinkled on top.
The dish will keep in the refrigerator for a few days, though you may need to add water when reheating. It does not freeze well.