Warm a dutch oven or large pot over medium heat, and add ½ cup butter, onions, garlic, bay leaf, thyme, and peppercorns. Stir until the butter is fully melted and cover.
Reduce heat slightly and cook for 5 minutes, or until the onions begin to soften. The onions should not brown at all.
Once the onions are soft, add the tomato paste and cook for a minute or so, stirring to incorporate the tomato paste into the butter. Add tomatoes, salt, and ground white pepper and cover again.
Continue to cook for about 30 minutes, or until the tomatoes are very soft.
Once the tomatoes have released all of their liquid, put the mixture through the finest die of a food mill. Return to the pan and add 4 cups half and half. Return to a gentle simmer.
Adjust the seasoning to taste, and let cool 2 hours, or put in the refrigerator overnight.
To serve, fill footed soup bowls to within ½ inch of the top with cool or chilled soup. Make an egg wash by whisking the cracked egg with a splash of water (a tablespoon is fine). Brush the rim of each bowl with the egg wash, then place a square of puff pastry dough large enough to cover the bowl over each bowl. Press down gently and brush the tops of each bowl with the egg wash. Bake in preheated 450F degree oven for 15 minutes. If they are not golden on top, bake 5 more minutes.
Notes
Alternative: cut frozen puff pastry dough into 2 inch squares and bake on a baking sheet at 400 degrees until they are crisp and puffed. Place over warm soup for puff pastry "croutons."