This chilled soup is arguably Hungary's most iconic summertime dish. The harvest season for sour cherries is short, and during those weeks, this soup is found on almost every restaurant menu and in nearly every home, where grandchildren are often given the task of pitting the cherries.
Heat a medium saucepan over medium heat until a drop of water flicked on the surface sizzles gently on contact. Add the filtered grapeseed oil, then immediately add the onion and fennel and cook, stirring occasionally, until the vegetables are slightly softened but not browned, about 5 minutes. Add the wine and dashi and bring to a simmer. Cook until the liquid is reduced by one-third, about 20 minutes.
Add the cherries, return the liquid to a simmer, and cook just until the fruit starts to break down and release their juices, about 10 minutes. Stir in the salt, remove from the heat, and let cool slightly.
Transfer the mixer to a blender, working in batches if necessary (the machine should be no more than half full), and puree until smooth. Pass the mixture through a fine-mesh sieve into a container and refrigerate uncovered until well chilled, about 4 hours.
Chill individual bowls in the refrigerator for at least 15 minutes, before serving. Ladle the soup into bowls and top each serving with a scoop of sour cream. Garnish with reserved cherries, pepper, dill, parsley, sunflower seeds, and grapeseed oil. Leftover soup will keep in an airtight container in the refrigerator for up to 4 days.