1. In small bowl, whisk together cider vinegar, mustard and shallot. Gradually drizzle in 3 tablespoons olive oil, whisking continuously until dressing is emulsified; set aside until ready to use.
2. Bring a medium-size pot of salted water to a boil over medium-high heat. Add potato slices to boiling water and cook 4 minutes; drain. Cut 1-inch off of bottoms of asparagus; discard. Cut stalks into 2-inch pieces.
3. Heat remaining 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add potato slices to skillet and cover; cook 3 to 4 minutes, stirring occasionally. Add asparagus pieces to skillet and stir to combine. Sprinkle potato mixture with 1/4 teaspoon each salt and pepper. Cover and cook an additional 4 minutes, stirring occasionally. Remove asparagus and potatoes to a plate. Very carefully, wipe out hot skillet with tongs and paper towels.
4. Season scallops with remaining 1/4 teaspoon each salt and pepper. Return skillet to medium-high heat and add half of butter, swirling to coat bottom. Add half of the scallops to the skillet and cook 1-1/2 to 2 minutes on the first side, then flip and cook 1 minute on second side, adjusting heat as necessary so butter doesn't burn. Repeat process with remaining butter and scallops.
5. Toss salad greens with 2 tablespoons prepared dressing and divide among plates. Toss asparagus mixture with remaining dressing and divide among salad plates, then divide scallops among plates and serve immediately.