Preheat the oven to 400°F (200°C).
Cut the butternut squash lengthwise in half (see step-by-step pictures in post above). Scoop out the seed and rub the cut-side with a little bit of water (or oil).
Place the butternut squash cut-side down on a baking sheet that you previously lined with parchment paper.
Peel the onion. Wrap it in aluminum foil or parchment paper and place it on the baking sheet.
Bake the squash for 45 minutes. Check doneness with a fork and make sure the thicker parts are tender. If it isn't soft yet, put it back in the oven for 5 to 15 minutes (depending on its size).
When baked, remove the squash from the oven and let it cool down for a few minutes. Optionally, peel off the skin or scoop out the flesh with a spoon. Cut the onion in half.
Add half of the butternut squash, half the onion and half the vegetable broth to your high-speed blender (e.g., Vitamix). Alternatively, add everything to a mixing bowl and blend with an immersion blender.
If the squash is still hot, unscrew the top part of the lid of your blender and start blending on slow. Increase the speed progressively to avoid splashes. Blend until creamy. Repeat with the rest of the squash, onion and broth.
Serve with some extra virgin olive oil if you'd like.