Wash the broccoli, cook in salt water until tender but firm, cool in cold water and place in a sieve to drain. In the meantime, prepare the batter and the pesto.   Separate the eggs for the batter. Combine flour, beer, egg yolk, salt and the oil in a mixing bowl and set aside. Now beat the egg white until stiff and fold gently into the batter. Puree the tomatoes for the pesto, chop the pine nuts and the basil, grate the parmesan and combine them all with the olive oil. Halve the chillis lengthways, remove the seeds, wash and finely chop the chillis and stir into the pesto. Season with salt and pepper. Pour the oil into a saucepan or a deep frying pan, dip the broccoli rosettes in the batter and deep-fry, drain off excess fat on kitchen paper and serve with the pesto.