Step 1In a small bowl, mix together the shallot, lemon juice, orange juice and olive oil. Season to taste with salt and pepper.
Step 1Discard the outer leaves of the lettuce. Wash with cold water and spin dry.
Step 2Peel the blood oranges. Using a paring knife, cut away the skin and any pith. Working over a wide bowl, cut segments out of the orange, slicing as close to the membranes as possible. Save some of the juice for the dressing. Set the orange pieces aside.
Step 3Scrub the beets and trim the stems. Cook them in boiling water for about 15 minutes, or until crisp-tender. Do not overcook. Cool, then peel and cut into quarter-inch wedges. Drizzle with a splash of the vinaigrette and set aside.
Step 4In a bowl, toss the butter lettuce with the vinaigrette, then divide among four plates. Add one-fourth of the beets and oranges to each place. Sprinkle each with pistachios and mint. Top each salad with one-fourth of the feta. Serve immediately.