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Cut fronds from fennel stalks and reserve.
Cut whole fennel in half lengthwise and core. Separate layers, reserving 3 or 4 tender inner pieces, and coarsely chop remaining fennel, including stalks
Sauté onions, garlic, and chopped fennel in oil over moderate heat, stirring frequently, until softened, 10 to 12 minutes
Stir in puréed tomato, 1/2 the sea salt and pepper and simmer, uncovered, stirring occasionally, 20 minutes
Pour tomato mixture through a fine-mesh sieve into a saucepan, pressing hard on solids and then discarding them
Whisk together egg whites, herbs, remaining sea salt and pepper in a bowl until frothy, whisk into cold broth.
Place cold broth on stove; bring to a simmer stirring gently to make sure clarifying mix does not stick to the base of the pot
As soon as the stock comes to the boil, do not stir any more, turn down to a gentle simmer.
Allow the raft to rise to the surface; the stock should clarify through the centre of the raft.
DO NOT STIR OR TOUCH THE CONSOMME AS IT IS CLARIFYING.
Cook broth at a bare simmer, uncovered, without stirring until broth is clear, 15 to 20 minutes.
Remove saucepan from heat and, disturbing raft as little as possible, carefully ladle out consommé through opening in raft, tilting saucepan as necessary, and transfer to clean fine-mesh sieve lined with a muslin. Discard raft.
Chill consommé, uncovered, until cold, about 1 1/2 hours.
Just before serving, season consommé with salt. Slice reserved tender fennel into thin slivers and toss with fennel fronds, pear tomatoes, and vinegar to taste.
Divide consommé and tomato salad among chilled bowls