Bring a saucepan of water to the boil and add broccoli and cauliflower. Cook for 6-8 minutes, or until tender. Drain, setting aside a third of a cup of the cooking liquid.
Heat olive oil in a large frying pan over medium heat. Add garlic, chilli and anchovies. Cook, mashing the anchovies with the back of your wooden spoon as they heat, but don't allow the garlic to brown. Add broccoli and cauliflower mashing some of the florets with the back of a spoon (you want a mixture of mashed and whole vegetables). When the broccoli and cauliflower have heated through, add half the parsley and the reserved cooking liquid. Bring mixture to the boil and season with salt and pepper. Remove pan from heat and set aside.
Bring a saucepan of salted water to the boil and add orecchiette. Cook until al dente, then drain.
Return sauce to heat and toss in pasta, heat through. Stir in parmesan and remaining parsley. Add a little water if the sauce is too thick. Spoon into large, heated pasta bowls, then drizzle with extra virgin olive oil to serve.