Preheat your oven broiler to high heat.
Prepare a baking sheet by adding either a sheet of parchment paper or a silicone matt or by just lightly greasing it to keep the pumpkin fries from sticking to the pan.
Peel and slice the pumpkin or butternut squash into slices that are around 1cm thick. Be careful when peeling the pumpkin as it can be hard to cut. You can either use a vegetable peeler or cut the pumpkin in half to get a solid base, and then with the cut side down on a cutting board, to keep the pumpkin stable, take a sharp knife and cut the peel off from top to bottom.
Cut the pumpkin slices into strips around 1cm thick.
Add the olive oil to a bowl with the strips of raw pumpkin. Combine them well until the pumpkin strips are completely covered with olive oil.
Place the pumpkin strips on the prepared baking sheet in a single layer, keeping a small space between them if possible.
Lightly season them with salt, pepper, and/or any other sugar or spice combinations of your choice.
Put the pan in the oven on the top near the broiler and broil at high heat until the pumpkin strips start to brown and get crispy edges.
Remove the pan from the oven and flip the pumpkin strips over and broil on the other side until crispy.
If you find that the pumpkin you are using is starting to burn but still is hard on the inside, bring the pan down a little ways and lower the heat. Continue to bake until the fries have reached the desired consistency. (Using butternut squash, I have never had this happen. I like to keep the oven time to a minimum to keep the fries from getting too soft.)
Remove from the oven and sprinkle with more salt, pepper, and any other herbs and spices that appeal to you, if needed.