Prepare your pizza dough. If you're making your own crust, follow these instructions. My preference is a pre-made dough that can be found in the refrigerator section at your local grocery store.
Preheat the oven to 400 F. Line a baking sheet with parchment paper and set aside.
Wash and peel the beets. Thinly slice the beets about 1/8" thick. This is easiest done with a mandoline slicer. Toss in 2 tbsp olive oil and 1/2 tsp of salt. Place beet onto the prepared baking sheet in a single layer and bake for 20 minutes, until beets are roasted and easily pierced with a fork. Remove from heat. Turn your oven up to 450 F.
Meanwhile, in a medium cast iron skillet, heat remaining 1 tbsp of olive oil over medium-low heat. Once the oil is hot, add onions and remaining 1/2 tsp of salt. Sauté slowly, stirring frequently, until onions are fragrant and golden brown, about 15 minutes. Remove from heat and set aside.
In a high-powered blender, combine all the ingredients for the cashew cheese and blend until completely smooth.
Place prepared dough on a pizza stone. Top with a thin layer of cashew cheese, spreading evenly to cover the bottom, leaving about 1/2" around for the crust. Top with a layer of caramelized onions followed by the beets, layering them so that they completely cover the top of the pizza.
Place the pizza in the oven and bake for 15-18 minutes, until pizza dough is golden brown.
Remove from oven and top with arugula and walnuts. Serve immediately.
Serving and Storing - Serve the pizza out of the oven. While the pizza is still warm, top with fresh arugula and toasted walnuts. Store leftover pizza in an airtight container in the refrigerator 1-2 days. Gently reheat the pizza in the microwave or oven before eating.
Recipe Tips - If you don't have a high-powered blender, soak the cashews for 6 hours prior to blending. This won't get them quite as silky smooth but it works in a pinch.
Variations - To save on time, consider buying pre-made pizza dough or a pre-baked pizza crust. In addition, prepare your cashew cream ahead of time. This can be made a day or two in advance.