Add the stems to the bowl of a food processor and chop until you have pea sized pieces. Add the basil, cilantro, garlic, and almonds, and process until just short of a thick paste. Add the goat cheese, and pulse until combined. Taste and add salt by the pinch until flavorful (you probably won't need much). Finally, with the processor running, drizzle in a small amount of olive oil. The quantity is really up to you. I don't particularly like an oily pesto, so I used only about 2 teaspoons; feel free to use more.

To store, place in a small bowl and cover with plastic wrap, pressing the wrap onto the surface of the pesto to keep out air. Keep in the fridge.