Boil a pot of water and remove it from heat once it reaches a boil. Add the cashews to the pot of water and allow them to soak for at least 30 minutes or ideally overnight. If you soak them overnight use cool water and store them in a closed container in the refrigerator.
Preheat the oven to 350 degrees and cooking the pasta according to package instructions. At the end of cooking the pasta set aside 2 cups of the pasta water before straining the pasta and set it to the side.
Cut the two heads (not cloves, entire heads) of garlic in half horizontally so you have half of each clove on each half. Place the garlic on a sheet of aluminum foil, drizzle ½ tablespoon olive oil on the open halves, then wrap up in the foil.
Cut the broccoli into bite-sized florets and place them on a baking sheet and drizzle the remaining ½ tablespoon on top and toss until coated in the oil. Place the garlic on the baking sheet and roast in the oven for 15-20 minutes on the middle rack.
Remove the garlic and continue to roast the garlic for an additional 5-10 minutes depending on your preference.
Combine the soaked cashews, 1 ½ cup of pasta water (you can add more to thin it out if necessary), garlic, crushed red pepper, nutritional yeast, lemon juice, and oat milk in a blender and blend until smooth and creamy.
Once smooth, transfer to a large pot and warm up over medium-low heat for several minutes until it is warm and has thickened slightly. Gently mix in the pasta and broccoli until well combined.