Use a sharp vegetable peeler to remove the skin from the butternut squash, then cut it in half, remove the seeds, and chop into 2-inch cubes.
Heat a large skillet over medium heat and add two tablespoons of olive oil. Once the oil shimmers and starts to smell nutty, add the squash cubes in an even layer.
Sauté the squash, stirring occasionally, for about 10 minutes until the edges turn golden brown and start to caramelize, filling your kitchen with a sweet, toasty aroma.
Pour in half a cup of vegetable broth or water, then cover the skillet with a lid. Let the squash steam gently for 8 to 10 minutes, until tender and soft inside.
Remove the lid and increase the heat slightly to evaporate any remaining liquid, allowing the squash to develop a silky, slightly caramelized surface.
Finish by squeezing fresh lemon juice or drizzling honey over the squash, then season with salt and pepper to taste. Add herbs or spices if desired for extra flavor.
Serve the sautéed butternut squash hot, with a crispy exterior and a tender, velvety interior, perfect as a side dish or light main.