Roast the Beets - this can easily be done a day or two ahead. Just cut off the stem (green part) and wash well. Place them on a sheet of aluminum foil, drizzle with olive oil 1-2 teaspoons and salt and pepper. Wrap up in the foil and bake at 375 for 50 minutes for medium sized beets. 45 for small 60 for large. Just let cool before peeling the skin. Just use a small plain knife and pull off the skin. If you don't want red fingers use gloves. Or after peeling them (and you will have red fingers - just use a light mix of bleach and water and the red will come off your hands). Just store in a baggie or ziplock/plastic container. Don't slice until you need them.
Salad - Now prepare the salad. In a medium size bowl add the arugula, red onion and pecans reserving some for a garnish. Now I don't add the apples or pears until right at the end. Just drizzle with lemon so they will not brown and set on a plate covered in saran wrap to the side.
Duck - First score the skin. With a knife cut cross marks on the skin side in order to release all the duck fat as it cooks. Just salt and pepper well. Then in a heavy pan such as cast iron, cold not heated - add 1 teaspoon olive oil and add the duck skin side down which is important. Turn the heat to to medium high heat, saute the duck. Starting from cold lets the duck render all the duck fat and give it a crispy crust. After about 10 minutes, flip and cover with a lid. Cook until 135 for medium rare. About 5-7 more minutes. Half way through you can drain some of the duck fat off if you want. Once done to medium rare, remove from the heat and cover with foil and let rest before slicing.
Vinaigrette - Remove most of the duck fat and just keep a little of the bits on the bottom of the pan for flavor, add the olive oil, mashed pear, garlic and shallot to the pan and cook until well combined 2-3 minutes. Add the white wine to deglaze the pan and cook another minute. Add the mustard, rice wine vinegar, apple juice, fresh thyme, salt and pepper and cook just a minute.
Put it all together - Add a couple of tablespoons of the vinaigrette to the lettuce and toss lightly. Make sure to add in the pears and apples at this point. Now slice your beets and duck. On each plate add your salad mix, then fan out the sliced beets (1 beet per person), and top with the duck thin sliced (1 breast per person). Top each with the warm vinaigrette and garnish with extra pecans and gorgonzola crumbles.