This bright and fresh first course will set the tone for the rest of the dinner. Red-and-white-striped Chioggia beets (also called candy cane beets) make a festive presentation, but if you can’t find them, use red or golden beets.
Place beets in a medium saucepan with cold water to cover. Bring to a boil over high; reduce heat to low, and simmer until beets are tender, 35 to 40 minutes. Drain and let stand until cool enough to handle, about 15 minutes. Peel beets, and cut into wedges.
While beets are cooling, use a mandoline or sharp knife to cut fennel bulb and apple into very thin slices. Place in a large bowl with beet wedges, arugula, parsley, and mint.
Whisk together oil, vinegar, zest, juice, salt, honey, and pepper in a small bowl. Drizzle vinaigrette over beet mixture, and toss to coat. Serve immediately.