Rinse salt cod well under cool running water. Place in a 1 1/2- to 2-quart jar and cover with water; cover jar airtight and chill 1 to 2 days, draining and replacing water at least six times. Drain fish. In a 1 1/2- to 2-quart pan, cover salt cod with water; bring to a boil, reduce heat, and simmer until fish flakes easily, 5 to 15 minutes. Drain; when cool enough to handle, remove and discard any bones and skin.
Meanwhile, in a 10-inch frying pan (or 5- to 6-quart pan) over high heat, frequently stir onion and thyme in 2 tablespoons butter until onion is browned, 6 to 10 minutes. Scrape into a bowl.
Add broth and potatoes to pan; bring to a boil over high heat, reduce heat, cover, and simmer gently until potatoes mash easily when pressed, 10 to 15 minutes. Drain potatoes.
In a food processor (at least 1 quart) or bowl, combine fish, egg, onion mixture, potatoes, cream, mustard, and pepper. Whirl or beat with a mixer until potatoes are mashed; pass through a tami and season to taste with salt and pepper.
In a buttered shallow 1-quart casserole (or four buttered 1-cup ramekins, or a ring mold) spread cod mixture. Level (equally in ramekins) with a spatula, then swirl the top with the tip of the spatula.
Break about 1 tablespoon of butter into tiny pieces and dot cod mixture evenly, lodging pieces in the crevices.
Bake in a 400° oven until golden brown, 10 to 12 minutes. Serve hot with Indian tomato chutney. Finish with a great quality olive oil – I prefer Nuñez del Prado cold pressed Spanish olive oil.