To peel butternut squash:

1. First, cut the ends off of the squash about 1/4-1/2 inch from the top and bottom of the squash. 
2. Then cut the squash in half where the neck meets the base, and peel the long neck of the squash using a vegetable peeler. Until you reach the dark orange flesh of the squash. 
3. Use a kitchen knife or vegetable peeler to peel the skin off of the base of the squash. Until you reach the dark orange flesh of the squash. 

To cut butternut squash:

1. To cut whole butternut squash into cubes: Cut the neck of the squash in half then cut into planks or half-moon shapes, then into one-inch cubes. Then cut the base of the squash in half, scoop out the seeds, and cut it into half-moon shapes, then into one-inch cubes. 
2. To cut whole butternut squash in half: Cut the ends off of the squash about 1/4-1/2 inch from the top and bottom of the squash. Then stand the squash upright and use a sharp kitchen knife to cut the squash straight down the middle from the top of the squash all the way to the bottom of the squash. Then scoop out the seeds and discard them or save them for roasting later.

To cook butternut squash:

1. To cook cubed butternut squash: Preheat the oven to 400 degrees F and line a baking sheet with parchment paper. Spread the cubed squash out onto the baking sheet, drizzle it with olive oil and season it well with some salt and pepper. Toss to coat it in the oil and seasoning. Roast the squash in the oven for 25-30 minutes until tender and slightly golden. 
2. To cook halved butternut squash: Preheat the oven to 400 degrees F and line a baking sheet with parchment paper. Place the two halves of squash onto the baking sheet, cut-side up, and brush each half with olive oil and season each with some salt and pepper. Place the halves of squash cut-side down and roast it in the oven for 45-60 minutes until fork tender. Note: the cooking time will depend on the size of the squash you are using. A 3-pound squash will take about 60 minutes to fully cook.