Toss scallions in olive oil and kosher salt until slicked all over, then spread them out on a half-sheet tray.
Set the broiler to high and broil the scallions until blistered and charred (about 5 minutes).
While the scallions cool, add crumbled feta, sour cream, kosher salt, black pepper, smoked paprika, and lime zest and juice to a food processor.
Chop ¾ of the scallions into ¼-inch slices and add to the food processor, discarding the root ends.
Pulse until everything is just combined (but still a smidge chunky).
Transfer the dip to a serving bowl; top with remaining scallions; and serve with Seedy Oat Crackers or crudités.
