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.
If using your own dough, MAKE SURE to sprinkle the bottom of the pizza stone with a bit of flour or cornstarch to prevent dough from sticking.