Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.
Toss butternut squash with olive oil, salt, and pepper. Spread out on the prepared baking sheet.
Roast in the preheated oven until browned on the edges, stirring halfway through, 20 to 30 minutes. Let cool to room temperature.
Meanwhile, prepare pumpkin seeds. Heat oil in a small frying pan over medium heat. Add pumpkin seeds, salt, paprika, and cumin. Cook, stirring often, until fragrant, 2 to 3 minutes. Add maple syrup, stir to coat, and remove from heat.
Combine balsamic vinegar, olive oil, maple syrup, brown sugar, garlic, salt, and pepper in a glass jar with a screw-top lid. Tighten lid and shake vigorously to emulsify dressing.
Layer mixed greens, persimmons, cooled butternut squash, feta, pomegranate seeds, and pumpkin seeds on a large platter. Drizzle 1 to 2 tablespoons of vinaigrette over salad and serve remainder alongside.
