Set a strainer over a large bowl.
Use a metal spoon to scrape the seeds and strings from the center of each melon half into the strainer.
Press gently on the seeds using the back of the spoon to gather the juices in the bowl.
(The juice from this part of the fruit is very high in pectin, a natural thickener found in ripe fruit, and is used to add texture to the soup.
) Discard the seeds and strings and set the juice aside.
Use a sharp knife to peel the melon halves.
Use a small melon baller or the knife to make ½ cup of teaspoon-size melon pieces.
Place in a bowl and season with the flaky salt and sherry vinegar to taste.
Set aside for 30 minutes.
Meanwhile, chop the remaining melon into golf ball–size pieces.
Drain and discard the excess liquid from the seasoned melon and set the melon “confit” aside.
In a pot over medium-low heat, combine the butter and onion and stir frequently until the butter has melted and the onion is soft and translucent, 25 to 30 minutes.
Add the large melon pieces and the reserved melon juice to the pot and cover with the lid slightly ajar to allow some steam to escape.
Turn the heat to low and cook, stirring occasionally, until the melon has softened but not disintegrated and the soup has reached around 160ºF.
In other words, sipping temperature: cool enough to take small sips, but too hot to gulp; about 30 minutes.
Working in batches, transfer the soup to a blender and puree until smooth.
Strain through a fine-mesh sieve (this is optional but will yield better overall texture).
Season with kosher salt to taste, then set the soup aside to cool to room temperature.
Store in an airtight container in your refrigerator until nicely chilled.
To serve, ladle the soup into six chilled glasses or four chilled bowls.
Top with the toasted almonds and the melon “confit.
” Drizzle with the almond oil and garnish with a chervil sprig.