Add all ingredients except for the pumpkin seeds and olive oil to your food processor. Turn on until mixture is pretty smooth (about 1-2 minutes), pausing and scraping down the sides of the food processor as needed.
Add the pumpkin seeds (1/2 cup). Cover the food processor and gradually pour in the extra-virgin olive oil (1/3 cup) as you pulse the food processor about 10-20 times, or until pumpkin seeds are finely chopped up and olive oil has fully incorporated into the sauce.
Store the pesto in an airtight container or jar in your fridge for about a week, or in the freezer for up to 6 months. Use on sandwiches, on pasta, on chicken/fish, or any other way you would use basil pesto!
Replace the pumpkin seeds with another seed, such as sunflower, or a nut, such as pine nuts, almonds, or walnuts, if you prefer. Go nuts! Hahaha. Hah.
Make it vegan by omitting the parmesan cheese and adding more salt. If you do this, I recommend toasting the pumpkin seeds (or nuts) to add more deep flavor and umami.
If you're sensitive to spicy foods, omit or decrease the amount of the crushed red pepper.
Traditional parmesan cheese may not be suitable for a strict vegetarian diet because it contains animal rennet. If you prefer, you can look for a suitable vegetarian substitute, such as a parmesan made with plant rennet.