To make the mozzarella sauce, drain the soaked cashews from the soaking water and rinse well. Add to a high-powered blender, like a Vitamix, with the remaining ingredients and blend until very very smooth. No bits of cashews should remain. Pour the mixture into a saucepan and heat over medium-low heat whisking constantly for about 4 to 5 minutes until it thickens and is gooey. Remove from the heat.
Meanwhile, cook the rigatoni in a large pot of salted water. Drain but do not rinse. Reserve a cup of starchy pasta water before draining.
Heat olive oil and all-purpose flour in a large pan over medium heat. Use a flat wooden spatula to stir it around until it thickens into a roux, cooking for about 5 minutes. Slowly pour the soy or oat milk in while continuing to push the mixture around with the wooden spatula or whisk to get it well combined. Continue to cook over medium heat until it becomes slightly thicker.
Add minced garlic, tomato paste, and gochujang stirring well to combine. Continue cooking the sauce for about another 5 to 8 minutes. Add more nondairy milk and/or some starchy pasta water, a small portion at a time, if the sauce becomes too thick. Cook longer if it's too thin.
Lower the heat on the pan of sauce, and toss in the cooked rigatoni. Combine until well coated in the sauce. If you feel it needs some reserved starchy pasta water to thicken and coat the pasta, add a little bit at a time, while continuing to heat it over low.
Lightly coat a 9 x 13-inch baking dish with olive oil. Add the sauced pasta to the baking pan. Dollop the mozza sauce all over the top. It won’t be a thick even layer but will cover almost all of the top of the pasta. Then add bread crumbs evenly on top.
Bake in an oven preheated to 400°F for 15 to 20 minutes until bubbling. Broil for 5 to 8 minutes to get the top browned and bubbling, if needed. The top should be browned and the mozza slightly puffed.
Before serving, garnish the top of the baked pasta with finely chopped parsley.