Combine gin, lemon juice, lime juice, simple syrup, heavy cream, egg white, orange blossom water, and vanilla extract in a shaker without ice (dry shake).
Shake vigorously for at least 2 minutes - this is the critical step that builds the signature froth; do not skip or shorten.
Add a large scoop of ice to the shaker and shake hard for a further 1–2 minutes until the shaker is very cold and the mixture is thick and voluminous.
Strain into a chilled highball glass without ice, pouring slowly to encourage the foam to rise above the rim.
Let the drink settle for 30 seconds, then gently pour the soda water down the side of the glass - this lifts the foam into the iconic tall, pillowy head.
Serve immediately with no garnish, or a simple orange slice on the rim.
Henry C. Ramos reportedly employed a relay team of 'shaker boys' during Mardi Gras to keep up with demand - each shaking the same drink for a stretch before passing it on, sometimes for 12 minutes total. The extended dry shake before adding ice is non-negotiable: it is what aerates the egg white and cream into the drink's legendary meringue-like foam.
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