Peel turnips, halve lengthwise and slice into half-moons ¼-inch thick.
Heat olive oil in a large cast-iron skillet over medium-high heat. Working in batches if needed, add turnips. Sauté, turning often and lowering the heat if necessary, until nicely browned and cooked through, about 8 to 10 minutes.
Season with salt and pepper, then transfer to an oven-proof serving dish. If not serving immediately, leave at room temperature for 2 to 3 hours, or refrigerate and bring to room temperature, before reheating in a 400-degree oven for 10 minutes.
To serve, mix garlic, capers, lemon zest and parsley; sprinkle over turnips. Drizzle with lemon juice.
