Cut the broccoli and stems into a bunch of pieces all roughly the same size. Toss the stems into the bottom of a saucepot, then layer the florets on top of the stems. Add a little water -- just enough to not quite cover the stems (and not covering the florets at all, ideally), cover the saucepan, and bring the water to a boil. Reduce to a simmer and cook until the florets are bright green and the broccoli stems are tender when pierced with a knife -- this doesn't take that long and you don't want to overcook it. Cooking will take around 10-15 minutes, but this can vary quite a bit depending on the size of your broccoli stems and florets.
Toss the broccoli into the food processor, reserving the cooking liquid. Pulse the broccoli in the food processor and begin seasoning to taste -- start with just a couple tablespoons of olive oil, a pinch of salt, a squeeze of lemon, a pinch of red pepper flakes, and so on, until you have a result you like. Use the reserved cooking liquid to thin the sauce if necessary. It should end up with a hummus-like consistency.
To serve, toss with your favorite pasta (I think this sauce works best with orechiette, but little shells, corkscrews, or penne would all probably be good substitutes). Top with toasted pine nuts and parmesan, if desired.