Heat the butter in a medium saute pan over medium heat. Add the bacon and cook until fully rendered and caramelized, 10 to 12 minutes. Remove the bacon from the pan and add the onions; sprinkle with salt and pepper. Cook, stirring occasionally, until the onions are browned and tender, around 15 minutes. Return the bacon to the pan along with the sage. Cook for 1 more minute.
Whisk together the pumpkin puree, eggs and cream in a large bowl. Whisk in the onion mixture. Pour into the prepared crust and bake until set, 30 to 40 minutes. Allow to cool for 10 minutes.
Whisk together the cheese, olive oil, vinegar and lemon juice in a bowl. Season with salt and pepper and toss in the arugula.
Cut the quiche into 8 equal portions. Top the quiche with the salad and serve.