In a small bowl, whisk together shallot, garlic, vinegar, olive oil, salt, and pepper. Set aside.
Bring 4 cups water to a boil in a medium saucepan. Cut off and discard bottom halves of asparagus spears. Cut tops into 2-in. lengths. Cook asparagus until barely tender, about 3 minutes. Drain in a colander and transfer to a large bowl of ice and cold water. When cool, drain and set aside.
In a large bowl, combine lettuce leaves and sprouts. Add half of the reserved vinaigrette and toss carefully just until coated. Divide lettuce and sprouts among 4 plates, starting with the largest leaves for the bottom layer. Sprinkle each pile of greens with asparagus, cucumber, bell pepper, and radishes. Drizzle the vegetables with a little more vinaigrette.
Place 1 tbsp. goat cheese on each salad and serve with remaining vinaigrette and sea salt for sprinkling if you like.
Note: Nutritional analysis is per serving.