Preheat the oven to 400 degrees F.
Put the oil and onions in a medium skillet and cook over very low heat, stirring occasionally, until onions are soft and caramelized, about 15 minutes.
Turn the heat up to medium and add the arugula. Cook until the arugula is wilted, about 1 minute. Season to taste with salt and pepper.
Spread the onion/arugula mixture over the crust, and top with generous, evenly-spaced crumbles of the goat cheese.
Place the pizza on the middle rack of the preheated oven and bake for 10-12 minutes, until the crust is heated through and the cheese is starting to soften + brown.
Remove from the oven, allow to cool for a minute or two, then cut into 8 slices and serve warm.