Place 1/2 cup of the cucumber in a blender. Add oil, yogurt, lemon juice, mustard, garlic, pepper, and 1/4 teaspoon of the salt; process until smooth, about 30 seconds. Cover, and refrigerate until ready to use.
Bring a small saucepan of water to a boil over mediumhigh. Add farro; reduce heat to medium, and cook until tender, about 10 minutes. Drain, and let cool.
Using a peeler, cut asparagus lengthwise into thin strips to equal 1 cup (about 2 ounces). Arrange greens, asparagus, and remaining 1 cup cucumber on a platter. Drizzle with dressing. Sprinkle with farro, goat cheese, walnuts, and remaining 1/4 teaspoon salt.