In a colander or a strainer, carefully wash the roe under cold water
Drain and peel off the thin film around the roe. Transfer to a medium-sized bowl.
Place the bowl with the roe over a pot or saucepan with barely simmering water. Make sure that the bowl with the roe doesn’t touch the water.
With a wooden spoon stir the roe for about 2-3 minutes until all of it is the same light pink color.
Let it cool for a little while.
Pour the oil into a measuring cup.
Keep the lemon or lime juice, and the club soda or sparkling water close to your work place.
Begin stirring with a wooden spoon in the same bowl where you partially cooked the roe.
Start with a teaspoon of lemon juice and after that is well mixed, add 2 tablespoons oil to stabilize the emulsification, transfer to a food processor.
Process, alternating a teaspoon of lemon juice and a few drops of oil at a time.
Repeat until all of the lemon juice and oil are incorporated and the mixture thickens.
To aerate and thin out, shake the bottle with club soda and add 1 tablespoon to the food processor and process briefly.
Then add salt, black pepper to your taste, and diced shallot.
With the processor running, add the remaining 1 tablespoon of olive oil in a slow steady stream.
Remove from the food processor and chill before serving. Keep refrigerated for not more than 2 days.