1. Preheat oven to 425°F.

2. Coat beets with a thin film of olive oil and sprinkle with salt and pepper. Wrap beets individually in aluminum foil and place on sheet tray. Roast in oven until beets give no resistance when pierced with a skewer, about 1 hour. Remove from oven and let cool. When cool enough to handle, peel beets and slice into ¼-inch-thick rounds.

3. Dry scallops thoroughly with paper towels. Heat a cast-iron sauté pan until smoking hot. (If you don’t own a cast-iron pan, any material that isn’t nonstick will work.) Add butter. When butter foams, sprinkle scallops on both sides with salt and pepper and, once seasoned, transfer immediately to hot pan. For first 30 seconds, do not disturb scallops. After 30 seconds, loosen scallops with a spatula and gently swirl pan in a circular motion to roll scallops, encouraging all surface areas of scallops to come in contact with bottom of pan. Cook until golden brown all over, about 3 minutes. Remove to a plate and cover to keep hot.

4. Add lemon juice to same pan and stir vigorously with a wooden spoon to release browned bits. Season to taste. Return scallops to pan and gently swirl pan to coat scallops with lemony sauce.

5. Fan beet slices on plates. Arrange scallops with their sauce over beets. Pile mâche on scallops, and garnish salad with lemon zest. Sprinkle with salt and pepper and grate a bit of Parmigiano-Reggiano over each plate. Serve while scallops are warm.