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Finely zest the lemons.
In a large saute pan heat the remaining 1 tablespoon of olive oil until hot but not smoking, add tenderloins to pan and sear on all sides, about 5 minutes total. (If you have a small pan, sear 1 tenderloin at a time.) Move pan with pork to the oven and cook until a meat thermometer reads 155 degrees F, about 6 to 8 minutes.
Heat a medium saute pan on medium-high heat with the butter in it. When the butter begins to brown add the lemon juice and cook for 30 seconds. Stir in the apples and salt. Saute for 3 to 4 minutes until the edges just begin to color. Add the honey and put in oven for about 15 to 20 minutes until the apples are soft and lightly caramelized.
Yield: 4 to 6 servings
Cook's Notes: Most applesauce recipes call for cooking the apples on the stovetop from start to finish. I prefer to start them on the stovetop and then finish them in a hot oven. The oven heat concentrates their flavors by drying and caramelizing them slightly. Although I have suggested a couple of apple varieties, you can use what good cooking apples are available in your area.