Preheat the oven to 375°F. Place the fennel on a rimmed baking sheet, preferably lined with foil or parchment paper. Drizzle over 2 tablespoons of the olive oil, toss, and spread out in a single layer. Season with salt and pepper, sprinkle with the Parmesan, and roast for 40 to 45 minutes until browned and tender. Let cool on the baking sheet to room temperature.
Meanwhile, make the salad. In a large bowl, combine the remaining 4 tablespoons (1/4 cup) olive oil, the lemon juice, vinegar, and salt and pepper to taste. Stir then add the spinach, arugula, and red onion and toss to coat with the dressing. Add the cooled fennel and toss again. Sprinkle with the pepita seeds and serve.