Heat 2 tablespoons of the olive oil over medium heat in a large frying pan. Add the onions and sauté for about 5 minutes until softened, stirring occasionally. Lower the heat a bit and add the garlic and red capsicum. Continue to cook, stirring often for 15 minutes.
In a food processor or blender, finely chop the almonds. Add the capsicum-onion mixture, the vinegar, and the remaining olive oil; blend all to a purée. Add the salt, black pepper and chillies. Blend briefly to incorporate.
Arrange a vegetable steamer over water in a saucepan. Bring the water to the boil and add the broccoli. Cover and steam broccoli over medium heat for 5 minutes or a bit longer, until it is tender as you like. Keep warm.
Cook the pasta according to package instructions. Drain, and return it to the pot.
Pour the red capsicum sauce, Parmesan, broccoli and basil into the pot with the penne. Heat the contents over medium heat until thoroughly combined and heated through. Add more salt and pepper to taste if necessary. Serve immediately.