Place the potatoes in a large saucepan. Cover with salted water and cook over medium heat until just tender, about 15 - 20 minutes. Drain. When still warm sprinkle 1 tablespoon of olive oil and toss to cover. Set aside.
In a separate saucepan cook the beets over medium heat for 45- 60 minutes, or until fork tender. The cooking time will depend on he size of the beets. Drain and let them cool slightly. Peel and cut into 1/2-inch cubes. When still warm sprinkle 1 tablespoon of olive oil and toss to cover. Set aside.
Mix potatoes, beets, shallot, green peas and corn in a large bowl.
In a small bowl or measuring cup, whisk together the mayonnaise, vinegar, mustard, and dill. Toss with the vegetables. Taste and adjust salt, if necessary. Add freshly ground pepper. Sprinkle queso fresco, if using.
Serve right away or refrigerate.