In the bowl of a food processor, blend the broccoli, basil, parmesan, garlic, almonds, pecans, olive oil, salt and pepper until semi-smooth. There should still be a few pieces. Set aside. Add a little more olive oil if needed if the texture seems too thick and adjust the seasoning.
Bring a large pot of salted water to a boil and cook the pasta according to package directions.Reserve ½ cup cooking water and drain. Set aside.
Meanwhile, heat the butter in a large frying pan, add the capers, the French shallot and the quartered figs, cook for 2-3 minutes. Add the pasta, pesto and cooking water, toss to coat well and cook for an additional 2 minutes over medium heat.
Serve on each plate with crumbled goat cheese on top. Pepper generously.