Toast the pumpkin seeds and sunflower seeds separately in a heavy skillet over medium heat, stirring often so they do not burn, until golden brown, 3 to 5 minutes. The pumpkin seeds will pop and puff up when they are ready.
Combine the toasted seeds, oregano, garlic, oil, salt, and a healthy grinding of pepper in a food processor and blend until smooth. Taste and adjust the seasonings as necessary. The pesto will keep for 5 to 7 days in the fridge or for 6 months or more in the freezer.