Cut the beets into ¼ inch thick rounds and set aside.
To make the vinaigrette, stir together the vinegar, ¼ teaspoon salt and ½ teaspoon pepper. Add the extra-virgin olive oil in a thin stream, whisking constantly until the dressing is smooth.
In a small frying pan, toast the chopped pecans over medium-low heat, stirring, until fragrant and starting to brown, about 5 minutes. Pour onto a plate to cool, and set aside.
Divide the curly endive and arugula among individual plates. Top with the beet rounds and drizzle with the dressing. Garnish with the orange zest and the toasted pecans and serve.