Heat 1 tablespoon oil in a saucepan over medium-low heat. Add leeks; cook until soft, 10 to 15 minutes. Transfer to a plate; cool.
Combine cooled leeks, cucumbers, water, bread cubes, crème fraîche, almonds, grapes, vinegar, and remaining 1 tablespoon oil in a blender; blend until smooth, about 1 minute. Strain through a fine-mesh sieve into a bowl. Cover the bowl with plastic wrap; refrigerate until chilled, 1 to 2 hours.
Season with cayenne pepper and salt; taste and add more vinegar if desired. Garnish servings with dill oil (see Chef's Note), thinly sliced grapes, slivered almonds, and fresh dill.
