Heat oven to 400 degrees. Brush squash with 1 tsp oil and season with salt and pepper. Roast cut side down until tender, about 30 minutes. Flip and set aside.
Heat 1 Tbsp oil in a medium skillet over medium heat. Add onion and cook, stirring, until tender, about 6 minutes. Add sage, thyme, beans, quinoa, and kale. Cook, stirring, until greens wilt, about 2 minutes. Season with salt and pepper.
Divide stuffing between squash halves and roast until golden, 15 to 20 minutes.
For each serving, sprinkle with 1 Tbsp hazelnuts, drizzle with 1 Tbsp oil, and squeeze with lemon.
Refrigerate stuffed squash in an airtight container up to three days.